Strange lines on my texture

I’m experiencing some strange lines when I’m close up to some of my foliage assets, my large beach grass in particular. They are not so visible when I’m farther away, though these will be rather large and the player will be able to get right up close to them, so the lines are visible in game. I’ve tried fiddling with the bias of my lighting but it seems to have no effect. These are alpha cards/cut outs if that helps at all, and I don’t believe it to be Z-fighting.

Any help would be greatly appreciated!

Images for reference of the actual asset