Must a parent with lifetime rights sign sale contract?

You mean a contract to sell a property in which the parent has a life estate? No.

If the children want to sell their future interest in the property, it is separate from the rights of the parent with a life estate. Similarly, the children do not need to be asked if the the parent wants to sell (or mortgage) his or her life estate to someone else.

On the other hand, if the buyers want clear title, with no life estate, then you have a different problem: terminating the life estate, by merging it with the future estate, and what's in it for you?