Laser fusion has nothing to do with civilian nuclear power generation.
It serves two purposes. One is to maintain sufficient number of nuclear scientists needed for nuclear weapon program (talent retention, so that they turn to other professions or sell their talent to other countries), the other is to serve as a platform for plasmas physics study to simulate nuclear reactions under conditions similar to hydrogen bombs.
LLNL is under the control of NNSA, National Nuclear Security Administration.
The Chinese laser fusion facilities (Shanghai, Mianyang, and Beijing) are for similar purposes.