I’d just stick to Lucy! It’s the most familiar way to spell it, and I know a lot of Lucilles that spell their nickname like Lucy - so I don’t see why it would be different for Lucina, even if there is no Y!
Honestly I don’t think you can go far wrong with any of them. Lucy is the most popular so nice and easy, but Luci and Lucie are also particularly intuitive written down, so I’d go with your gut and which one you are most drawn to!
I’d say [name_f]Lucy[/name_f] is just fine - simplest, tidiest and probably the most intuitive if [name_f]Lucy[/name_f] is well-known where you are. After all, there are plenty of names in which the nickname has extra/different letters to the full name (think [name_f]Grace[/name_f] nn [name_f]Gracie[/name_f], [name_f]Margaret[/name_f] nn [name_f]Maggie[/name_f], [name_f]Isabella[/name_f] nn Izzy). [name_f]Luci[/name_f] could easily work too (and [name_f]Lucie[/name_f] actually) - so whichever you think will be easiest or that you like best!
[name_f]Lucy[/name_f] is fine if you prefer it. No different from [name_f]Katherine[/name_f] to [name_f]Katy[/name_f] or [name_f]Elizabeth[/name_f] to Lizzy/Betty etc.