I think Solari is a must when playing lucian. Really OP item with him. Basically you will crit ad and ap after using an ability which is what lucian does the most in the game.
I see a lot of players building bloodthirster instead of sheildbow and I think sheildbow should be the go-to item this patch since riot added more damage to the game. I'm not doubting your ability to play safe since you're challenger level player, bit it's saved me a lot somced I started ranked.