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.
JUST conservation of energy, sure... consider a universe composed of a ball moving at constant speed in random directions.
But conserving everything our physics conserves means you're using our physics. It's not even a hypothetical if you do that.
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.