No, you will not be able to use it on your iMac.
There are two sections in the Lion license that discuss "Permitted License Uses":
Section A states that Lion on your new Mac Mini will follow the "Standard and Preinstalled Apple Software License," which allows you to use and run
(1) copy of the Apple Software on a
single Apple-branded computer at any
one time. [I listed what was relevant, emphasis added]
Section B discusses the License from Mac Store, which allows you to install it on as many computers as you own/control.
Added screenshot of license below:
Edit: I'll also add my 2cents. Because you didn't purchase it from the MAS, I don't think it will let you download it for free. It's like if you look at the MAS pages for Garageband, iPhoto, or iMovie on your new Mac. They'll probably be listed for $14.99 each, not "installed"