What makes Lucian Mid viable?

Of the ADCs, Lucian is perhaps the strongest duelist in the early game and has one of the best level 2 & 3 spikes as well as one of the best one item spikes. His dash makes him far more mobile than most ADCs and his E -> passive-empowered autoattack -> Q -> passive-empowered autoattack combo lays down a lot of burst.

Early game, particularly against mid champions that rely on scaling, Lucian is a powerhouse. He's meant to be a situational pick that can force trades against champions that rely on positioning and zoning.

As for what makes other ADCs less viable in the midlane, they're all missing a little something. Most ADCs aren't very mobile and the ones that are aren't mobile in the right way or are weak for other reasons. Draven can get a big speed boost from his W but it's just a simple speed boost not a dash and he's easily punished with zone control. Vayne has a dash but her waveclear is atrocious. Ashe has strong waveclear with her W and use of Runaan's, but she has little to no mobility. Tristana has mobility from her W and natural waveclear, but her early game damage just can't match up most mages.

Lucian has a bit of everything that makes up a good midlaner. Good mobility from his dash, strong burst and trade power from his combos, good waveclear with his Q, passive, and ult. So as far as ADC comparisons go, it's both where he's strong (very good early-game lane bully) and where he's not weak.