I want to download Lemmings on my computer for free.  What site can I go to to do so?  

You don't search a lot as I can see! Look at some abandonware websites to find all games for free. Then come back here because of the corrected version of Lemmings with the good safe-fall distance, the corrected version of LemEdit if you want and the corrected version of Customized Lemmings too. Don't forget Cheapo Copycat where you can make your own graphics! ;)

Anything you want (except Cheapo) should be on the site in my sig...

Abandonia. It has Lemmings, Oh No More Lemmings, and Lemmings 2 the tribes  ;)