My starter runs but does not engage the flywheel. Does it have to be out of the car to clean and lube the starter drive?

 

Most likely, I can't see being able to back off the nuts enough to gain access to the Bendix, even with some sort of oil like Tri-Flow.
You may try, the worst that will happen is that you'll realize you can't get in there and you will have to remove it.
If it won't even engage, it may need more then just a cleaning.

 

I ordered brushes and springs for the starter. The shop that does my work says they can remove the starter to clean the starter drive and change out the brushes and springs. The starter runs but does not roll the motor.