Lucy's a brat. Simple as that.
She has always been seen as kinda a "genius" kid, but while the teachers kept praising her, and she skipped up to her sister's grade level, the other kids didn't really like her. She grew up very haughty, sassy, and frankly, pretty annoying.
She learns quickly, but in terms of her social life, when she starts her Pokemon journey, she is not well-socialized in the slightest. She has successfully stood up for her sister before, but was also often picked on for being younger, which only fueled her tiny rage-filled body to prove that she can be better than them while being younger.
This also led to her having a very "rushed" personality. She feels any time she's not doing something productive is time wasted, and while she does her best not to put those expectations on her Pokemon as well, sometimes it slips through the cracks and she can't help putting pressure on her precious partners.
SPEAKING of her partners, I've finally decided on Lucy's initial Sinnoh team.
Amber, her female Chimchar, a shy Pokemon who is quite lonely, struggles to socialize with other Chimchar her age, since they tend to be quite energetic and playful and she's a lot more reserved and peaceful.
Sunny, her shiny female Swablu, who is also a spoiled brat, and may as well have directly peeled Lucy's personality right off of her. She was hatched in an Egg-trade "hot potato" incident involving a Shiny Hunter (the same incident through which Fluffy was hatched; Sunny was the one in the Shiny-marked Egg). Sunny is much more aggressive than her two more softhearted brothers, and she's not afraid to flaunt her golden feathers. She, too, needs to get knocked down a couple pegs.
Ruby, a Misdreavus from Eterna Forest. Lucy initially caught him with the goal of creating the "perfect Contest team", and sought Misdreavus for its intelligence and haunting beauty. However, Ruby refused to listen to her for the longest time, constantly pulling pranks, messing up her choreography, and overall doing his best to piss her off (which worked, she wasn't exactly great with regulating her emotions and was very prone to tantrums). Ruby doesn't listen to her for a WHILE until she catches her final Pokemon.
Cammie, a female Hippopotas from Pastoria's Great Marsh. Lucy was initially extremely turned off from having a Hippopotas on her team. I haven't decided exactly how she catches her, but Cammie is incredibly attached to Lucy regardless, and despite her clumsiness, is actually very resilient in battle. In witnessing Cammie defend her in her natural environment, Lucy finally has an epiphany about how she should be coordinating her performances: catering to the Pokemon's styles, rather than forcing them to cater to hers. Cammie earns Lucy her favorite Ribbon by starring in her first "themed" performance, the Safari theme. (I need to decide which exact ribbon it is, because god I have to do research on all the contest halls in anime sinnoh now oml)
As she grows up, Lucy's personality shifts from that of an impatient, petulant brat, to that of a dignified, yet snarky princess type. She doesn't let people get too close, but she entertains them with witty remarks and rarely talks about herself unless it's in relation to her siblings, whom she's also very proud of (if a little bit jealous, but she won't say that part out loud).
You could say Lucy's kinda a tsundere, and honestly, that's not too far off from the mark. However, she is also still learning how to be more self-aware, and while she wants to impress others, she also understands the consequences of acting too hastily after making some grave mistakes in her childhood. She may not be a Pokemon Professor, but she still has the inherent will to learn and grow, which is why Uxie favors her so strongly.
I like to think Legendary Pokemon look at certain humans, but they don't just randomly "choose" them for no reason. There will never be the "perfect" candidate. Sometimes the perfect candidate has to be made. In order for that to happen, they need to pass their trials. Like exams, or an interview period, except more hardcore and mindfucky.
Lucy's arrogance is what ends up hurting her siblings, and she is challenged to look past her pride and glare directly at her flaws, unblinking and unflinching. When that happens, she's humbled deeply and has to work harder to make up for the trouble she caused trying to bite off more than she could chew just because of some kids in her fourth grade class.
Mind you, this wouldn't just be happening in Sinnoh. This kind of self awareness is probably going to take at least two to three years to really sink in. But when it finally does, she's already caught up to Sylvia's level by the time she finally turns ten, and earns her proper Trainer license, perhaps a little precariously.
In short, modern Lucy (18 yrs old) knows she's "all that," but also her ego is usually mostly for show, because despite her attitude, she actually has a lot of guilt in her for how she used to behave when she was a kid.