Who is the safest adc but can put out a lot of damage? Lucian?

Lucian is pretty safe, but it requires a skilled player to know when to go in and when to back out. Ezreal is really safe because he can just spam Q and has a god like blink he can use for escape. Caitlyn is safe as well, due to her having the highest base auto attack range in the game and has Q has high damage and high range. Tristana has growing auto attack range over time, but will take a while to grow beyond Caitlyn's. She gets resets on her W, which is an engage and escape tool. Corki has his package which will result in him dashing a ridiculous distance and his standard valkyrie will allow him to dash a decent distance as well.

urgot

is safer than cait

= highest AA range of all the champions

are the safest adcs.

has the strongest pushing power and the highest long-range DPS lategame of the three; is the strongest lane bully of the three; has the best poke and burst of the three.

Also worth mentioning is , who is surprisingly safe and effective with an ADC build (thanks to her 3 dashes on a short cooldown and built-in CC)