I have no shut off valves between the outgoing water of the water heater and the valve for the hot for the washing machine. I do have shut a shut off valve for incoming water to the water heater, but the incoming line branches to the Lennox hot water boiler furnace. When I shut off the house incoming water to be able to replace the valve for the washing machine do I need to do anything to keep from getting air into the pipes of the furnace?

No. Just close valve on incoming water line.

Agree.