He is a squishy champion, early game he does tons of damage so take advantage of that with his q to lock a minion to hit the champion. After every skill he does a fast double shot with his passive, so when you chase a champion Lucian becomes a lot stronger. He also comes with a dash so it becomes a lot easier to chase plus his "w" that when lands increases his movement speed. So he can get kills easily. With his ult it shoots in the direction you choose it so make sure you can keep up and hit them constantly with it, by the time you have the phantom dancer and last whisper it will burst enemies hp down fast. He gets low on mana fast and easily, so try to get blue as much as possible before deciding initiating or team fighting.

I made my purchase order like this because its more comfortable, and seems to me added on right to go against other enemies. It add's the best kind of crit along with speed, and makes the life steal great already. I save infinity edge for last because its expensive and by that time its late game and you can farm that gold easily by either minions or secretly jungling since nobody uses jungle late game hardly. This Build also helps to make tanks against Lucian pointless almost too. you can burst the tanks down with regular hits or using your dash around them to get more shots in.

So far i have used Lucian against dozens of champions and he kills them easily against all, his skills clear minions and mobs greatly and makes it better for team fights, his ult lasts awhile too so that for team fights or clearing minions when stuck to inhib clears everything easily. Only champion i have a problem with was Leona, if they are good and know how to combo their skills they will kill you before you can get more than 3 shots off, so try to avoid a 1v1 with her.

I use Ignite and Flash so when i try to push bottom down or anywhere if i get ganked or i know i cant win the 1v1 or a close fight i will lower them down as fast as possible and if i know im going to die i will ignite so that i can kill them along with me, its worked a lot with Lucian. Along with Lucian's "e" i can use flash if i get ganked without having ignite so i can get farther away and twice the distance.