NLW, ask your lawyer and tell him/her your fears. Ask what could possibly be in H's head and if there could be ulterior motives in this.

I would also ask lawyer if the suggestion that H draw up the agreement would be a better solution.

You can say that "my lawyer has advised me to do it this way"

I smell a "I didn't say that at all" coming. Maybe invite H to a meeting with L and a notary, ask him what he agrees to and get a notarized version of the conversation. Ask your lawyer for a recommendation of how to proceed