NO. The lasers are immaterial. You could use a hammer to cause the initial fusion (in fact ... [1]). The point of ignition is to have fusion powered by fusion, NOT by lasers. We want fusion of two atoms cause at least 2.000001 other atoms to fuse, and then raise that number. Not even by much 3 will definitely do it. If Q > 1, then this must have happened, there is no other explanation. That's the big advance. The point is to have the fire burn after we've lit the match.

You want to use lasers to initiate some fusion, you can do that using a tabletop laser lab (although magnetic confinement and big voltages is much simpler).

So this is the first machine where we're sure: it wasn't fusion caused by lasers, it was fusion caused by neutron pressure! Where did that neutron pressure come from? From other atoms fusing!

Note also that the sun does NOT do this. Fusion inside the sun is powered by falling atoms converting their falling energy first into heat then into singular fusion events, which essentially explode and throw a lot of atoms back up. Then the cycle begins again. Fusion inside the sun is a self-limiting reaction, which is why stars don't just blow up once, but "burn" over a long time. All the fusion inside the sun really does is slow down gravity for a little bit, then immediately stop. Gravity is producing the heat from the sun.

[1] https://en.wikipedia.org/wiki/General_Fusion