Greedi faucet is ok
https://github.com/Greedi/litecoin-faucet but it's the only one I can vouch for. It works (mostly) but you'll need to be reasonably comfortable with command line MySQL to get it working properly. The instructions are absolutely piss-poor, so expect a few headaches if you try it.
Unless your faucet is going to be the biggest thing since sliced bread, you won't need to worry about DigitalOcean boxes not being able to handle the load. Self-hosting through them is far better than most alternatives, and is a million times better than trying it with a cheap web hosting plan.
Thanks for the feedback. If it's the biggest thing since sliced anything I'd be shocked, haha. What is your opinion of just a simple manual faucet, maybe using google docs or something to have people fill out a form with their wallet, and then manually sending out coins once a day or something?