Did the weather change a lot between shooting? If it was hot when you shot the old scope and cold now that could account for some. Also, your 100yd zero could be ever so slightly off and accounting for the rest. As long as you can now repeat your dope from zero to range and back i wouldn't worry about it.

Did you zero the new scope? Did you change to a 20moa base? Are you shooting the exact same ammo? Changing scopes will not affect your trajectory. If you zeroed the rifle after installation of the new scope everything should be good. If not, one of the scopes is not

Technically you wouldn't know if they NEED lapping until its done as the process reveals the severity of the high and low spots in the machining (or finish). Lapping is simply a practice of maximizing ring to scope body contact. Id be willing to wager they DO "need" lapping based on how inconsistent the cheaper rings usually are, however the practical use of lapping the rings on a lower cost optic/rifle combo may not yield any visible results. In other words if you are building a $1500 rig to bang steel with then dont worry yourself with it. If your $12000 competition rifle is a source of income then by all means.....

I don't understand your question. You don't lap the scope, you lap the rings. I have lapped my mount without any issues. As always check spacing between the mount and caps before you lap to make sure there is enough room. Some cheaper rings/mounts don't have much room for error.