What should I do with my duplicates?

If it's not a unit you plan to use regularly, the best use for them is to send them home for feathers. If you plan to use that unit often, you should get them all to 5 stars then fuse them. If you fuse them before 5 stars they will loose the stats bonuses from fusing when you eventually upgrade them to 5 stars. When you fuse a unit it gets (+1) added to its level (40+1), up to a maximum of (+10)(40+10). Sometimes you might want to have two of the same unit in a team as well depending on what you are doing and what challenge maps get added in the future. You get plenty of free barracks space so it doesn't hurt to hold unto things.

For your specific case with someone like Lyn, I would recommend fusing them, check too see which one will have your preferred stat spread here (https://fireemblem.gamepress.gg/fire-emblem-heroes-iv-calculator). Lyn needs 700 sp to learn astra and galeforce so the extra sp from fusing also helps.

It depends on a bunch of factors, but here's my general approach:
- If you really like the character and intend to use them a lot, merge.
- If you don't really care about the character but they have useful skills, use them for Skill Inheritance.
- If they have no useful skills, send them home.
I would not suggest leveling up a second copy unless you REALLY love that unit.