How did Luc come back to life?

If you remember correctly. In the first Universal Soldier, The original Unisols had major conflict with their human sides. (Constant flashbacks)
Once those particular Unisols were taken off line, only the human side of those soldiers remained.
In Universal Soldier The Return, Luc continued having those flashbacks of his death. The movie does explain that he has once experienced death.
If you pay close attention to the end of the first film, you will see his lack of need for 30 degree refridgeration. Luc was more human than he was Cyborg. He had feelings, and memories of life.

In the Unisol II project. There were no emotions that could indicate that these Unisols had any memory of who they once were.

It was weird to see Luc able to live a normal life (having kids, etc.) after being re-animated. On top of that, he no longer needs to be cooled down or having "superhuman" powers like breaking concrete walls etc.