Ok, after I replied here I got my Core Duo upgraded to a C2D Mini and tried installing Lion. There are a few ways but I just took out the Mini's drive and put it in an external SATA case. Installed Lion then put the drive back in the mini. After that you boot into Snow Leopard and zap one file in system/library. After that Mini booted up and I registered Lion with Apple. Works GREAT. Quite fast and considering the early Minis only take 2GB RAM, I am impressed.
To the OP, if you want to try lion on your C2D older Mini, let me know and I will give you a few tips.
This also proves that if you buy Lion from the App store (Not a Lion that comes with a new Mac), it's $29.99 for your registered Macs and not $29.99 for each Mac you upgrade.
PS, be sure the Mini has a large hard drive as you need Snow Leopard installed to at least zap that one file. I have two partitions, one with SL and one with Lion and an external for Time Machine backup.