A hepa filter air cleaner would probably do the trick, along with a good amount of elbow grease.
Lots of towels, a bucket of water and a few friends would make short work of the mess.
Better to do it now, when the house is almost empty, than to try cleaning around all your stuff.

I wouldn't use towels or cloths you intend to launder. I'd use disposable ones you could seal up and toss in the trash. Normally I'm against throw-away stuff, but for cleaning up potential lead-contaminated dust, I wouldn't want to clean those rags in my washer, nor would it be ethical to take them to a commercial laundromat and leave any residue for the next unsuspecting user.

I'd do physical removal first before running the HEPA air filter. No point in contaminating your vac or a HEPA machine with stuff you may be able to remove, permanently. After you washed and dried any surfaces that can take it, then get the machine going to clean out any remaining dust particles in the air. And don't shake mops or dust cloths outside your home as that will just contaminate the soil underneath where you track it back in again, or ruin it for growing food.

Molly~

The standard for removing lead dust is HEPA vacuum followed by washing surfaces with TSP solution and then rinsing. There is also a product called Ledisolv (you can buy it online) which is supposed to be as effective as TSP but less toxic.

Yes, do the cleanup while the place is still relatively empty. On the other hand, it might not be so bad. I've gotten a certain satisfaction cleaning after a renovation. It really provides a nice end to a project.

The whole idea is not raising dust and causing it to be airborn. Pick up the chunks. I used a push broom to slowly push the major grit and dust up (with all doors shut.....or if the room didn't have a door, suspend an old sheet over the opening to keep the dust confined), instead of vigorous back and forth sweeping with a normal broom. Then I'd also use disposable material, moistened, to get as much loose tuff up as I could. Then I'd vacuum it with a machine with a hepa filter. Then wash it well. Then repeat with a rinse, whether the cleaner says it's necessary or not.