I decided to post this build after it got me level 6 lucian and 1 level 7 shard in a single day. If you play it right it shouldnt be too difficult to get an S with lucian. Just know this build is a mostly passive-aggressive build meaning that if you play really aggressive this isn't for you.

Most people who play AD carry are going to look at the ignite and say you should take heal. Reason I have ignite is so that you can have your support take heal and you can secure that the other AD carry wont get away with ignite.

Some people have told me to take Heal instead of flash. Yes lucian has his dash E but it cant go over all walls and it should be used With your Flash since your E isnt that far. Using them both allows you to catch enemies even if they flash away.

Most lucian players know lucian is an AD carry who farms most of the game. This ties into the passive-aggressiveness I stated in the introduction. How I made this build was for people to be able to just farm all of laning phase and only go in if they get ganked by the ally jungler or if they dive too deep. If you play like this they will eventually screw up and give you a free double kill.

The items I have given you are pretty close to the recommended with the exception of Botrk. My reason for that is your first back should be for a Bilgewater Cutlass. This allows you to have a little lifesteal as well as Percent max health damage for those tanks. It also allows you to secure a kill with its Minimum 100 damage. So how I go along with my items are I always go Botrk first then Statik shiv. After that its up to you depending if you need more Crit damage or you are having mana problems. You would also build beserker's grieves in there somewhere of course for the movespeed and attack speed. If you need more damage in the late game, you can sell the boots and botrk for a death's dance and a bloodthirster.