My own thinking is to do the dry firing before taking the side plate off and lubing.
Seems like the smoothing action of firing will be less if there is lube between the metal parts.
Just my thoughts on the subject, I don't have any way of verifying them.
In the long run, the action will improve with use.
I just took the side plate off of my new M640 Pro, after 150 rounds of live fire, and about 1000 dry fires.
It was not dirty inside and I didn't see any metal shavings. I think there is less chance of shavings in guns made with MIM parts. They are not machined, as I understand things.
Next up is my M686 SSR. I just put a little anti corrosion lube on the pivots and sliding parts. Maybe not too little, as I know that I will need to wipe up a little excess for a week or so. I have been using Corrosion-X for this process.
The revolver has a different feel after lubing, as expected.
Best,
Rick