A large area of my lawn was almost entirely taken over by wild garlic (at least I think that's what it is; it looks and smells a lot like onion . . .). I did some research, and have been working on them slowly (it takes more than a year to get complete eradication).
Best treatment regimen for me, is 2,4D (I used an amine formula), twice a year. First time right as the early ones pop up, after the snow is gone. Second time at least a month later, but before leaves are on the trees (so now is good).
I would beat the clumps up with a square stick, to bruise the surface, and I added a wetting agent to the chemical (i.e. sticker spreader) before spot spraying the bunches.
Skip those two steps, and whatever you apply just rolls off their waxy surface.
Then wait at least a week for the chemicals to work their way down to the bulb, before mowing them down.
Since last year, it's about 75% gone.