Lucian is a very distinct ADC, as hes majorly focused in casting spells, they can trigger a outrageous ammount of damage, his passive also provides you a instant double attack after casting a spell even if it doesn't hit your target.
His ultimate (The Culling) is considered to be the best ADC ultimate in team-fights, sice it haves a big ammount of AoE damage, placing your ult correctly followed by a full combo can end a team-fight easily.

Farming / The Laning Phase

Your laning phase is very alterned, since you dont have a very good laning phase, but you have a good damage output early in the game (combo's dude), when you come back with your brutalizer, you'll need to farm a lot, a farmed Lucian is a strong Lucian, at about 20 minutes, you can go full agressive, roam from time to time, and of course, if you have nothing to do, farm, remember that ADC's need to farm a lot.
If your lane is hard-pushed and your mid-laner doesn't rely's much in the Blue buff, you'll probably want to ask your jungler for the it.

Skill Sequence / The combo

Q >> AA >> E >> AA >> W >> AA >> R

For 1v1 or 2v2

W >> R >> Q >> AA >> E >> AA

For team-fights