Upgrading new Mac Mini to have SSD. Do I have to buy Lion, or can I just re-download from App Store?
Macs introduced after 10.7 was released (and mid-2010 to mid-2011 Macs with a firmware update) support internet recovery: if you start up with a new hard drive, you are shown a gray screen like this and something like the contents of the recovery partition are downloaded over the internet:

http://support.apple.com/kb/HT4718

If you happen to encounter a situation in which you cannot start from the Recovery System, such as your hard drive stopped responding or you installed a new hard drive without OS X installed, new Mac models introduced after public availability of OS X Lion or OS X Mountain Lion, automatically use the OS X Internet Recovery feature if the Recovery System (Command-R method above) doesn't work. OS X Internet Recovery lets you start your Mac directly from Apple's Servers. The system runs a quick test of your memory and hard drive to ensure there are no hardware issues.
OS X Internet Recovery presents a limited interface at first, with only the ability to select your preferred Wi-Fi network and, if needed, enter the WPA passphrase. Next, OS X Internet Recovery will download and start from a Recovery System image. From there, you are offered all the same utilities and functions described above.

You can then install the OS your Mac came with for free or restore the old installation from a Time Machine backup.