I have done this on my own mowers only about 6 times. Take top cover off mower and you will be able to take clutch apart and clean and lube it but not with grease. That will make it stick. Use a spray lub. Watch out for coil spring, if it unravels its hard to get back on. Hope this helps. I am no expert. I just saw where no one else answered you.
Just clean it real good, I wouldn't put any grease/oil inside starter clutch with the ball bearings. Ball bearings need to be dry and clean. I usually dab just a little grease near end of crankshaft.
Inspect where metal contacts metal or plastic, ball bearings- inspect.
Installation reverse taking it apart.