Is It safe to have underfloor heating with lead paint?

We’re in the process of renovating an old farm house with a old section and a new side.

Because the house has a hydronic heat system we are looking to convert to underfloor heating throughout. Right now it’s a mix of forced air in the old part of the house and underfloor Heating in the new.

We just hit a bump though, having discovered that all the 2nd floor rooms have lead painted floors underneath a plywood subfloor and then a laminate or engineered flooring (depends on the room).

We plan on keeping the old board sealed under a newer floor, but should we look to remove the paint first? Will the underfloor heating cause the paint to off gas or something?

Thanks,