My first impression is that Lukashenko has played a blinder. He was as good as gone in Friday if Putin fell but now he has a mediator status, the additional (temporary) protection of a portion of Wagner's power, and some bargaining chips with Russia in order to deal with the Ukraine situation. All while he can seek to gain the trust of Prigozhin who -while alive- is a candidate to replace Putin if things don't go to plan, therefore extending his regime's protection beyond Putin.
That is, unless he is asked to off Prigozhin. Then "between a rock and a hard place" doesn't even start to describe the situation he will be in. And recent events/declarations suggest this is a very likely scenario.