Yes, any Intel Mac mini with at least 2GB of RAM will run Lion Server. In fact, if you take a look at Apple’s Servers Made Easy page, you’ll see a Mac mini shown right there at the top. They now sell a mac mini specifically built for Lion Server. The page reads:
Best of all, you don’t need expensive hardware to run it — you can use an Xserve, of course, but you can also use a Mac Pro, an iMac, or even a Mac mini.