I read that the upgrade to OS X Lion is not intended for Mac Minis, is this true?
Is there a way to upgrade a Mac Mini with an Intel CPU to OS X Lion?
Yes, you can update a Mac Mini to Mac OS Lion.
What you heard was incorrect, Mac Mini's are upgradable, just like any other Mac. Lion requires a Core 2 duo processor and 2 GB memory to run, so any Mac produced after circa 2007 will be fine.
This depends on the exact CPU in your Mac mini. As stated on http://www.apple.com/macosx/how-to-buy/ "[y]our Mac must have an Intel Core 2 Duo, Core i3, Core i5, Core i7, or Xeon processor to run Lion".
Since the 2006 Mac mini Models, however, shipped with a Intel Core processor (http://en.wikipedia.org/wiki/Mac_mini_with_Intel_Core#Specifications_2), it is not possible to install Lion on these machines.
An easy way to find out whether this applies is to select "About this Mac" in the Apple menu. There, you can see whether you have a supported processor.