So if Lucian mid is a thing, what about the others?

It isn't, and those aren't either.

Varus/Kog mid

Due to changes from Armor Penetration to Lethality, no.

Or old Ashe mid.

What the fuck, no....

mid is to counter most of the push wave then roam mid laners. He is slippery enough to dodge damage, has okay wave clear, and is a lane bully. Varus/cog are too imobile, they cant avoide ganks while also pressureing the lane like lucian can.

Ap tristana mid.

No, the reason lucian mid is a thing is for he has mobility, mobiltiy is highly valued in mid lane, to be a mid laner you need a way to either cc people so they can't reach you.

examples E, someone ganks you, you just e stun them and walk away or you just have dashes and walk away with something like a E

Many people thought mid was going to be a legit thing and had every right to think so, but than they realized something. Tank junglers like or can just dive you under tower and use guarentee cc onto you, and boom your dead.

Unless we see some dramatic game changes like to items or buffs/nerfs to other champs we wont see varus mid again any time soon.