After reading her she does seem a tad underpowered, if only for her lack of firepower, defense options,  and lack of actual powers or tech that could give her an extra edge, such as energy manipulation and such. Things that could help in this particular fight if you refuse to buff her up in any way would be to lift the charging time on her railgrenade launcher, and more viable cqc options. Nothing fancy or over the top. You'd be surprised how much you can actually cut with a bare bones lightsaber or chain blade.

You also mentioned how she is meant to incapacitate rather than kill and I can see what you mean. Though for someone like L you'd likely need a more aggressive style to actually accomplish that if you arent going to have lots of support abilities. So in general I think she could stand to have a few more actual offense options such as extra weapons or tech, or at least supporting abilities that make her tankier or support her "capture, not kill" skillset.