@Chris Seveney and @Pat L. thank you for replying. I intend to do everything to the letter of the law, and as part of the sales contract, we are doing the full lead inspection with X-ray fluorescence, and any remediation that needs to be done. The seller has conceded to pay for it, since she knows she was negligent in not getting it done. Not only that, but the selling agent is the one who got the tenants in there without any lead tests, disclosures, or registering the property with the county. They could have been hit with some very large fines.
It sounds to me that although I would not be liable for any previous tenants' lead poisoning, I could still be sued by them since anyone can sue anyone for anything.
All things considered, I think the risk would be small of this happening. The lawyer suggested having the sellers sign an indemnity agreement, but I'm not sure they'd sign it, and also wouldn't stop anyone from suing me.