I doubt Luka had anything significant to do with cooking this up at all.And what is Luka gonna do? Offer the FSB hit team a drink? Write a slightly awkward letter to Vlad "Vova" Putin?
I'm inclined to believe this was hashed out internally by Russia. Belarus presented a sort of solution where Prigozhin/Wagner was offered an out that kept them safe and maybe even useful and able to continue activities. Luka's reward for compliance was to be credited as peacemaker, given a day in the sun and improve his reputation as a statesman, etc.
I don't really believe Lukashenko is an independent leader anymore - Russia propping him up after the protests following the last Belarusian election left him more a puppet of Russia than ever.