If the Earth and the moon became tidally locked, would this last theoretically forever (assuming no external gravitational force modifies their orbits, for example, ignoring the effects caused by the Sun)? Or would their orbits would change?
If the Earth or Moon are still slightly non-spherical (due to rotation and the fixed tide) then if any fractionation occurs (heavy stuff sinking towards the middle) then the orbit will expand very slightly.
I suppose, theoretically, the Earth-Moon will radiate gravitational waves which will reduce the energy of the system and cause the orbit to shrink. But I wouldn't hold your breath waiting for that to happen.