If you have the gigawatts of electricity required to run the inertial fusion lasers, there are probably better ways to use that power to get around. Massive ion engines, or powering the pumps for a nuclear salt water engine, maybe, depending on how exciting you want your ride to be.
Inertial containment fusion relies on firing a laser at an extremely precisely machined piece of heavy metal (called a hohlraum), heating it until it emits X-Rays, and using the X-Rays to create 2 implosion shockwaves in a tiny pellet of tritium + deuterium that have to meet in the dead center, so that where they meet they can start a fusion reaction, and ideally have the fusion reaction consume the whole pellet before the shockwaves dissipate enough to stop confining the plasma. A few microseconds after the laser blast, you get a puff of helium (+hydrogen if the reaction wasn't complete) and a mangled piece of metal, and some heat that in principle you could capture somehow, though no one has yet tried. Then, you throw away the now useless hohlraum, get a new one and a new pellet and you fire again for another little burst of energy, over and over.
The hohlraum is the biggest problem here: the level of precision needed to achieve the exact geometry inside the pellet to actually ignite a plasma means that every hohlraum is (a) extraordinarily expensive (currently in the millions of dollars range), and (b) entirely useless after a single shot - while continuous operation for a 1500 MW plant is estimated to require ~20 hohlraums/second).
For a spaceship design, this would mean that your engine would have to include a smelter and high-precision machining bay to constantly create new micrometer-smooth hohlraums from spent ones. Not even close to a promising technology.
NIF also has an expendable blast shield in from of each mirror of the final optics. These mirrors have to be in line of sight of the explosion. If you tried using something like this in space, without that shield the expanding plasma/hohlraum fragments would go right out though the vacuum to hit the mirrors. Even slight imperfections there will explode under high energy pulsed laser irradiation.
I'm a software engineer who saw a few videos on YouTube, and read a few articles on this topic, I don't think I am the right person to ask about this, sorry.