Similarities between Toki Pona and Lojban
Toki Pona and Lojban are two engineered constructed languages with speaking communities and very different goals. Toki Pona is a minimalist language based on simplifying your thoughts to fit the vocabulary of 140 words. Its grammar is similarly minimalistic. It has a simple sentence structure, not many particles and no affixes at all. Lojban is a logical language, one designed to express logical statements in its grammar and lack structural ambiguity. It is not at all minimalist, having over 3.5 times more particles than Toki Pona has words in total. It has particles for just about any grammatical function or marking you can think of.
So you may be surprised to learn that, having learned both languages, I consider them to be strikingly similar. They both have traits in common that English lacks for what I think are similar reasons.
Overall character
These are the big picture similarities. They are the cause of the specific similarities discussed later.
One class of root words
Both languages throw root words into one class, with usage determining their interpretation as a noun, verb or modifier. Both achieve this slightly differently.
Toki Pona's contentives
Most Toki Pona words cover broad semantic categories and have interpretations as nouns, verbs and modifiers relating to these categories in some way. For example, the definition of "moku" is:
eat, drink, consume, swallow, ingest; food, edible thing
These all relate to food and eating in some way. A very frequently cited example of Toki Pona's ambiguity is "mi moku" meaning "I eat" or "I am food", as Toki Pona doesn't have a copula. Note that it's not possible to predict how the meaning of a word changes between noun and verb usage and this must be memorised with each word.
Lojban's verbs
Lojban's only class of root word is verbs. These are defined in an unusual way, resembling sentences with blank spots given numbered Xs for nouns. For example, klama means:
x1 goes to x2 from x3 by route x4 with means/vehicle x5
"klama" is about as complex as verbs get, having 5 blank spots (arguments). Most have fewer than this! The blank spots are how Lojban creates nouns. The articles (lo/le) in Lojban select the first place of a verb and turn it into a noun. This avoids the need to memorise unpredictable changes in meaning for different words. For example, "lo citka" can only ever mean "an eater", it cannot mean "a food", which would be "lo cidja".
Concepts that are nouns in English are verbs in Lojban that include their copula. For example "cidja" means:
x1 is food for x2
This is as much as a verb to Lojban's grammar as the entire rest of its root word dictionary. The exact same grammar that works with "klama" works with "cidja". In other words, Lojban makes no distinction between being and doing. This also means that while Lojban does have a copula, it is barely ever used. Verbs contain "to be" in their definition.
Greedy phrases
In English you mostly know where a noun phrase ends because a lexically defined noun appears at the end of a string of lexically defined adjectives. Context and word order alone are usually sufficient to know how an English sentence is structured. Toki Pona and Lojban both take a different approach, because zero-deriving modifiers from contentives and verbs means that phrases are "greedy", they keep expanding unless explicitly separated.
Toki Pona phrases
Modifier phrases are the main way that Toki Pona stays expressive with only 140 words. Toki Pona has noun-modifier order. "jan pona" literally means "person good" but actually translates as "good person", since English is an adjective-noun language. You can keep adding root words onto phrases indefinitely and every following word modifies the whole phrase to its left:
small red car tomo tawa lili loje ((room move) small) red
Lojban tanru
Lojban's "tanru" are phrases just like Toki Pona's, where one word modifies another through juxtaposition. Lojban's order is backwards from Toki Pona, with the verb determining the place structure (and therefore most of the meaning) occurring last rather than first. However, Lojban still groups modifiers to the left. Just like in Toki Pona, root words can be added onto the end indefinitely since all are in the same category and they cannot, on their own, indicate the end of a noun phrase or start of a predicate.
intensely-red type of car kandi xunre karce ((intense) red) car
Keeping open question words in place
English fronts question words. This means that when asking a question, the syntax of the sentence is shuffled in some way that brings the wh-word to the start of the sentence. "You want what?" becomes "What do you want?". This is not the case in Toki Pona or Lojban, which prefer to keep question words unmoved.
Toki Pona's seme
The question word in Toki Pona is "seme" and it can go in the noun or verb positions of a sentence.
This is/does what? ni li seme?
This is good for who/what? ni li pona tawa seme?
Lojban's ma and mo
Lojban has different question words for every possible type of question. It has many more than just "ma" and "mo" which are noun and verb questions respectively. But those are the question words that most directly correspond with "seme" and just like it, don't require any change in word order.
This is/does what? .i ti mo
This is good for who/what? .i ti xamgu ma
Word order
Both Toki Pona and Lojban are similar to each other but also English in word order. Toki Pona has subject-verb-object word order and also tends to move preposition phrases to the end of sentences. While Lojban's word order is flexible, it defaults to a very Englishy order of putting the verb second, after a single noun and then putting all other nouns after the verb.
I give a book to you at the library.
mi pana e lipu, tawa sina, lon tomo lipu. I give a book, to you, at building book.
.i mi dunda lo cukta do bu'u le ckusro I give a book you at the library.
Specific similarities
As a result of the similarities in overall character, Lojban and Toki Pona have some very similar grammar.
Predicate markers
English doesn't have a predicate marker because it doesn't need one, not usually anyway. A predicate marker tells you where the verb in a sentence starts. This seemed like such an obviously artificial feature to me (having only seen it in Toki Pona and Lojban) that I assumed it was something that only existed in conlangs for a good while. I've since learned that Tok Pisin has a predicate marker. Natural languages are always stranger than I expect!
Toki Pona's li
The word "li" in Toki Pona separates third-person subjects from their predicates. It is essential to Toki Pona's grammar to allow for speakers to stop adding description to the subject and start the verb.
A big cat wants a fish. soweli suli li wile e kala.
Toki Pona allows for a subject to have multiple predicates attached to it by repeating "li".
A hunter sells food and goes to a house. jan alasa li esun e moku li kama, tawa tomo.
Lojban's cu
The word "cu" in Lojban terminates any nouns before the predicate of a sentence or clause. This is very similar to "li" and when Toki Pona speakers learn Lojban, it's very useful to be able to say "remember 'li'? it works like that".
A fish eats a person. .i lo finpe cu citka lo prenu
However, it is never actually obligatory in Lojban. It is usually used when the noun before the verb is one that uses an article, as opposed to a single-word pronoun. This is because pronouns self-terminate and don't start a greedy tanru phrase.
I run. .i mi bajra
Lojban only permits one "cu" per clause. This is a very helpful rule for certain deeply-nested sentence structures. Attaching multiple predicates to a single subject is still possible, but requires conjunctions.
A hunter sells a food and goes to a house. .i lo kalte cu vecnu lo cidja gi'e klama lo zdani
Phrase bracket particles
The default way that both languages group together modifiers in phrases means that it's impossible for multi-word phrases on the right to modify single words to the left. A phrase with the structure "A B C D" will always group together as "((A B) C) D" when what you want may be "(A B) (C D)". Both languages have words for this exact purpose of regrouping modifiers, a type of particle that has no direct counterpart in English.
Toki Pona's pi
Toki Pona's particle "pi" is used to override Toki Pona's default left grouping. An example is "tomo telo nasa", which translates to "crazy restroom" because "tomo telo" groups together and is finally modified by "nasa".
crazy restroom (tomo telo) nasa (room water) crazy
Putting a "pi" after "tomo" allows for "telo nasa" (alcohol) to modify "tomo", creating the meaning of "bar". These two very different meanings are only distinguished by the grouping of modifiers.
bar tomo pi (telo nasa) room (water crazy)
Using multiple "pi" in one phrase is ambiguous and considered bad style. It is unclear whether both pi phrases apply equally to the head of the phrase (flat pi) or the second pi phrase applies only to the contents of the pi phrase it follows (nested pi). The example given in sona pona is "lipu pi sona mute pi toki Inli". Is it a book of much knowledge of English, or a book of much knowledge and English?
Lojban's ke-ke'e
Lojban's particle "ke" does pretty much the exact same thing as "pi", but appears in opposite situations from "pi" due to the opposite word order of tanru compared to Toki Pona phrases.
catcher of big dogs barda gerku kavbu (big dog) catcher
The meaning of the phrase without pi in Toki Pona has to use "ke" to get the brackets on the right of the phrase.
a catcher of dogs, who is big barda ke gerku kavbu big (dog catcher)
Unlike Toki Pona, mulitple "ke" particles unambiguously nest into each other. Conjunctions are needed to achieve the "flat pi" meaning from Toki Pona.
small school for girls which is beautiful melbi ke cmalu ke nixli ckule pretty (small (girl school))
Unlike Toki Pona, a terminating particle "ke'e" closes the opening bracket created by "ke". Sometimes, the entire "ke-ke'e" structure may be replaced with "bo" as this marks a gap between two verbs to be interpreted as grouping together first before the usual left-grouping rule is applied.
small catcher of big dogs cmalu ke barda gerku ke'e kavbu cmalu barda bo gerku kavbu small (big dog) catcher
Analysis
Toki Pona is vague, not ambiguous
With a few small exceptions such as preverbs, prepositions and nested pi, the structure of a Toki Pona sentence is usually not ambiguous because of very un-englishy particles tagging parts of sentences such as "li" and "e". Most of Toki Pona's multiple interpretations come from its words covering board "semantic spaces", fuzzy clouds of meaning that are clarified through the addition of modifiers and context.
Toki Pona and Lojban both solve ambiguity in similar ways
Both being SVO isolating languages with greedy phrases, both languages use similar very obvious solutions for terminating phrases. Lojban has terminators, articles, prepositions and the predicate marker "cu". Toki Pona has "en", "li", "e" and prepositions marking the starts of phrases in sentences. The biggest overlap is predicate marking, but both languages also have particles exclusively for regrouping modifiers.