I know this is not a common scenario, but for the few people that upgraded a Mac originally equipped with a Core Duo processor to a Core 2 Duo processor, here is the procedure. I have an iMac version 4,1 that I upgraded years ago, and it worked. The person who found the solution had an upgraded Mac Mini. You will need a second computer that is Lion capable for this tip to work.
As always, Make sure you have a backup of the original install! This worked for me, but always be prepared for the worst.
I made, and used, a Lion Mac OS X Install ESD on a thumb drive. Instructions to make one can be found all over the Mac centric web sites. Then follow this procedure:
Mac OS X Hints