First of all, as
you HAVE to run Mana band and Gathering Storm as second tree. I dont know if you do it so I wanted to tell you that because Mana Band on him is needed.
Second, as bad as it seems you need to play more adc games to reach a decent level, there's a part that it's just "git gut".
The other part is using your characters strenghts in a interlligent way, which means that you can strictly only use mana as Lucian to only farm when you are zoned or to Q the wave to push the lane, other tactic that you must take in count is to use W to get the Mana Band proc as soon as posible, even starting with W and not with Q it's a good idea since at rank 1 both skills deal similar dmg and it's easier to land W.
For the rest, you have to kill majority of the minions with autoatacks and if you feel that doing that you get your lane pushed too often to your turret it means that you are either playing against Sivir or that you are only last hitting minions when you should be hitting every single aa that you can to minions not only to heal with DSword or the early VampiricS that you get.
And if doing that you lose too many minions you just need more games on Lucian. He is really strong now, like, disgusting, so play him before he gets the nerfs he deserves.