Is the use of a lock in amplifier with a signal generator appropriate and practicable?
I'm quite sure it is appropriate and practicable.

For modulating the generator, I have, however, some concerns:
In optics setups employing a lock-in often use shutter-wheels to modulate the (light) source; especially if modulating the source itself would be problematic or impossible (indandescent bulbs, daylight, starlight). That way continuously working (light) sources can be used.
The shutter wheel provides also the sync signal for the lock-in (e.g. from a separate fork light barrier). 

Switching the signal after generation by shutter- (or reflector-) wheel (or other means more appropriate for microwave) has the advantage that the generator can work continuously avoiding artifacts by modulating it at generation (e.g. frequency/power instabilities).  

Maybe this could be also important in your microwave application. Maybe not; if modulating the generator is not a problem.