I was wondering if it was possible to do the non-lethal option for the Lord Regent and when you see him being arrested, is it possible to kill him then? If so, how is this mentioned in game?

I'd say it's definitely an assassination.

I dunno where it happened ( maybe Sokolov ) but I got a "target neutralized" once, and still managed to kill the guy, like by dropping him and he broke his neck or something. Got a "target assassinated".

What happens if you kill Sokolov? Game over?