I have an A-Frame lake house that sits out over the water, built in the 1940s. The telephone poles used for the main supports are in poor shape and need to be repaired. To completely remove the poles would possibly require demolishing the house. Any suggestions on possible fixes?

Most lakes have some sort of rules governing what can or cannot be done on them or near them. I would suggest you start with your local government and see if you can even to anything to do.

Supports of this nature are repaired and replaced all the time without need to demolish the structure. Temporary supports are put into place while the main supports are replaced. It's not a DIY job. Consider acquiring 3 quotes from qualified contractors.