Ideas and concepts I have gathered so far through this account for this fic in non linear fashion (put under cut because of spoilers):
Light can carry injuries with him into the next cycle, they will not disappear over time
L will think that he is transported into different universes instead of a real time loop because of how drastic Lights mannerisms sometimes shift (the kiss™ will be the biggest reason for this assumption)
Light will at some point kill himself, this will reset his injuries but leave him with scars of his death
None of the other death note owners are in this world, not even the ones he doesn't know about yet and who aren't owners yet. (Yes this means he hasn't seen his father in ages and just assumes he is around.)
The above point will only be a hint for the readers, since Light and L don't know of any other death note owners yet
L will kill himself in front of Light shortly before his time is up. This will shift the time of his death to this point. When Light kills him too, this again shortens the time of the loop (might make the initial loop time longer in the fic itself)
L does not get any scars from his deaths and doesn't carry injuries with himself to the next cycle
Light will plan out a whole murder over several cycles, just for L to kill himself in front of him (as mentioned before). This will also be the time they both realize that they both remember the loops and that they are in them together
There will be one more kiss before they realize that though
This will be a tragedy, no real happy ending. Either they find out how to get L out and only L or they stay trapped forever together.
The solution to get L out would be for Light to die in his place, as in saving him from mortal danger and taking the figurative/literal bullet (depending in what situation they are)
No one seems to notice the missing people except for Light and L, so at some point they will notice that Lights father and Mello aren't there anymore. And that no one seems to even register that around them. This will not help them.
Even when I have fully figured out why exactly they are stuck in this situation, I don't plan to let the characters ever really know, for the audience I'm on the fence, depends on how good any explanation would fit, even crumbled in as context clues.
I will add more over time through reblogs :3