Spotsy, it IS possible to install Lion. To prove it, I'm typing this from a Mini that was once a 1.5 Core Solo, upgraded to 7200 and running Lion right now.
The trick is to install Lion on your drive from another (Lion-capable) machine. Either take it out and set it up temporarily as a USB drive, or remote into it using Firewire. Install Lion from the other machine, and then (crucially) go into /System/Library/CoreServices on your new Lion drive/partition, and remove the file
You should then find that once back in your Mini, it boots into Lion successfully.
NOTE: do all major Lion software updates BEFORE you put the drive back in your Mini, because a major update will put the PlatformSupport.plist file back. (This is a file that tells Lion which machines NOT to install on; Apple does this as a cheap solution instead of looking for the presence of the Core 2 Duo.) Or you could put a small partition with Snow Leopard or earlier onto your drive so you can always boot into that to repair the Lion drive if it ever gets broken by an upgrade.