Massachusetts still has lead in older homes and apartments. It is not an ideal situation, but I don't think you NEED to do anything unless one of the kids tests positive for lead. If there is no chipping paint and he does not let the kids suck on the woodwork it may not be a problem. The expense comes in IF they test high for lead, and even still there would likely be a delay looking at their primary home first.
We had a problem a few years ago when a couple who had lived at our unit had a child who tested high, and even then they needed to retest them 2 months later to be sure it was not a false positive. So we had a few months to figure out what the child might have gotten into and fix the situation in the meantime before the state stepped in. We were able to offer the family another apartment in a newer building in the meantime as well, just in case the second test was also high. But as it turned out the second test came way down because of all of the remediation we had done after the problem was first discovered.
We now have that unit 'lead encapsulated' which is much cheaper than remediation. Our 2 kids grew up in our unit (where only half of the lead has been eliminated) without any issues. Long story short, do not panic, the kids are not there that often. If he knew that there was lead in the unit prior to moving in I do not believe you have to be lead compliant UNLESS there is a problem with his kids testing high unless things have changed in the last 5 years.