While it won't be an issue on most CD-based games (because ones on CD rather than DVD tend to be older), some of them may still suffer from a CD key issue if patrons want to play the games online. A number of them (such as Starcraft, Diablo and the like) only allow one online account per CD key, which makes it impossible for any user to play at the same time as another user with the same CD key. Since patrons could install and/or copy the discs, that could come up. Online play is often a perk on those older games, though, rather than an integral component of gameplay, so it would still allow them to experience the full story (if one exists).
Newer games sometimes require an "always-on" internet connection, even if they're not digitally-managed through services like STEAM. Most of the Electronic Arts ones require an Origins account, while others just require that you remain connected to their servers for as long as you're playing. EULA notwithstanding, I think that could be one of the biggest difficulties in loaning them out (and it's why stores that sell second-hand games, such as Gamestop, generally don't buy/sell PC titles).