AFAIK Lagrange points are not fully stable, so any debris cloud will likely disperse into the Solar orbit, which is kinda big.

None of the ideas in the sibling comments (to my post) will work, because they ignore the fact that enemies will employ counter-measures which may cause debris to be formed. In the extreme case, a nation's military may decide to deny the area to anyone rather than lose their own access, intentionally creating such a debris field.

You'd have to fill the volume of at 25,000 Earths (or more, that's just my napkin math), where orbits aren't stable for more than a year or two, with enough debris to hit something a few meters across. No using explosions to do this either because debris with more than a few m/s aberrant velocity would be ejected from the Lagrange point even faster. Seems unlikely.

The entire thing is unlikely. I'm just pointing out that you can't claim space 'cleanly' when your adversaries are actively opposing your claim. To play devil's advocate further though:

As the 'defender' you likely don't need stable orbits. A year or two of denial might buy you what you want. You also don't need to ensure a collision against a single small target, you just need enough debris to make use of the area cost prohibitive in terms of risk.

Rendezvous, attach booster, and deorbit, or just fly away?

Only reasonable way at the moment would be some kind of satellite capture system that nobody has publicly demonstrated.