With Lathyrus latifolius you would have to dig the crown out, since it's a perennial plant. Or maybe nail it with a suitable spray, perhaps glyphosate. Try searching "pnw weed control", see if the online handbook mentions it.

My dad's hit his accidentally a few times while trying to Round-up some other stuff, so yeah glyphosphate would work. Best time to do it too is when the plant is just starting to go dormant; as it takes down nutrients for overwintering it'll take the herbicide with it!