I don't see any direct link between determinism and conservation of energy. You can have one or the other or both or none. You could have laws of physics like "when two protons collide, they become three protons", determinist but without conservation of energy.
As for "libertarian free will" I'm not sure what you mean by that, but free will is concept that must be dissolved, not answered "it exists" or "it doesn't exist", and anyway I don't see the link between that and the rest.
I don't see any direct link between determinism and conservation of energy. You can have one or the other or both or none.
You can have determinism without conservation of energy, but I opine that you cannot have conservation of energy (plus the other things that are conserved in our physics) without determinism.
This is a thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. The previous thread is at close to 500 comments.