Across 854 ranked games on patch 16.21 in Master and above, Lucian mains win 54.3% of their games in the bot lane.
Their most common build appears in 89.3% of those games and wins 54.9% of its 763 games.
It starts 
two Health Potions and 
Doran's Bow, completes 
Essence Reaver, 
Infinity Edge, 
Lord Dominik's Regards and 
Navori Flickerblade in that order, and takes 
Gluttonous Greaves.
One other build is played often enough in the bot lane to be measured on its own.
In the bot lane, Lucian mains fare best against 
Ezreal (won 68.8% of 32 games), 
Tristana (won 70.6% of 17 games) and 
Kalista (won 71.4% of 14 games).
Their hardest matchups, the champions that counter Lucian, are 
Corki (won 20.0% of 10 games), 
Jhin (won 37.5% of 40 games) and 
Jinx (won 38.1% of 21 games).