this is--complicated.
1) I don't know CA but MA has some of the strictest lead laws in the nation so it may be comparable. You may be looking at "strict liability" meaning any kid in that apartment that has elevated lead levels can hold you responsible, they don't have to prove that it was from the house and indeed it very likely wouldn't be.
2) with the tenants aware of this and needing it remediated you are going to have to do so, pretty much immediately if there is a kid in there or about to be. In MA I think you have 90 days before your liability kicks in. Don't quote, me this is from memory and I'm not a lawyer...but its something like that. This is going to be true even if your seller is provably at fault and you can hold them financially responsible. It is your problem now. Oh by the way, this often applies to any child under 6 just visiting :)
3) First call to a lead remediation company which can examine and make recommendations. Its not always grotesquely expensive. There is interim control, painting only certain areas etc. often around door frames and older windows...but it can be tens of thousands of dollars in a worst case scenario.
4) Second call to a qualified attorney who specializes in this area. Pay him/her, do not go cheap and find a generalist or a brother in law or what have you. Let them guide you.
5) Get moving quickly on both ends (the remediation and the attorney) immediately and my gut is you will be able to hold the seller accountable. This is one of those rare areas where it can be pretty cut and dried and in their best interest to provide you some financial relief. And they are flush from the sale now as well.
You never know, it might be a long ago citation for a minor thing that was painted over and this will be a trifle, but....
6) Get the tenants on your side by doing everything within deadlines and keeping them in the loop. Its going to matter. FYI you will likely be responsible for providing them housing during the entire remediation process, short or long.
7) Seriously, people have many ways of dealing with this before its a documented issue, but once it is public it has to be handled properly. You are tremendously exposed. It may be next to nothing but don't be shocked if the bill is all out of keeping with what you think of as the scope of work. The company performing the work takes on the liability and they are going to charge you for it. DO NOT get the same work done by an uncertified company even if its just as good...it doesn't cover you and will hurt your resale value.
8) I'm writing this from a liability perspective. The medical issues surrounding actual lead poisoning are devastating and you have a moral obligation to deal.
9) I'm talking about liability more than health because we all grew up in houses with lead paint and actual poisoning was rare. And even pre 78 houses have had so many renovations stuff is often buried under layers of changes and isn't a practical problem with reasonable parenting and reasonable maintenance. This cuts both ways though--for something to be elevated to public record means it often gets heightened attention.
10)'acceptable' levels have been lowered and lowered and so even though kids may not have had major exposure as youths the standard is much different now. Acceptable levels have ranged from 20s and are now at 2-4 to give you an idea of how different things are now.
Good luck, do not panic, but face head on and quickly