Tuchel should be an immediate upgrade, as Frank really isn't a big team coach yet and Chelski isn't the club to learn on the go. Of course, Tuchel is also volatile and I'm gonna assume that they are gonna be looking for a new manager 2 years from now when he inevitably burns bridges with management. Then again, that's pretty much par for the club.
It was a mistake to hire Lamps with one year experience at a little club in the first place, but hopefully he gained some good experience from this to find success elsewhere. He still can be a good coach, he just needs an environment that affords more patience for his growth to happen.