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Yes. We caught the boat over and stayed in one of the cottages on the island. There is a campsite there too but being on a small island it'd be pretty grim if the wind and weather was bad, you'd want to bag a camping spot in the shelter of the wall if possible if you were camping.
There's a very small shop that does convenience store basics but if you have any dietary requirements etc and plan on self catering then I'd recommend bringing food with you just in case the range in the shop isn't very big. We visited a few years ago so this may have improved by now. They also have a pub which serves food and seems to be one of the main social focus points of the island.
I'd say 3 days is enough to see everything at a relaxed pace if you're walking. We walked around the Northern half of the island one day and the Southern half the next. The letterboxing trail will take you round most of the points of interest and clues for this can be bought in the shop. Obviously there's birdwatching and climbing to be done too which could take up a lot of time if those are your sort of things.
The only bit we didn't get to was Rat Island which is accessible at low tide however it's over slippery seaweedy rocks and we weren't confident we'd get there and back before the tide came in, plenty of people manage to do it though.
Anyone done a trip to Lundy before btw? Found the guidebook for pennies up here in a second hand bookshop so had to get it.