Any polyurethane sealer should work fine. I'd use a couple coats to be safe. Are you actually going to use it to feed your kids? If so, I'd buy one of those lead test kits at Home Depot - first verify whether the finish is actually lead-based, and then after sealing, test to make sure you can't pick up any lead on the chair. I have to say that I personally probably wouldn't use a lead-paint high chair for it's intended purpose even if sealed, but I wouldn't have a problem sealing it and using it for display or as a doll high chair or something.

Good luck!

A good washing with warm water and ammonia is the first step. Flush the wash water down a sanitary drain (toilet).

Two coats of Spar Urethane will seal it until it's either chipped or sanded.

As lkplatow says, I wouldn't use it to seat a child.

Michael