Roger Nicholson's "Nonesuch for dulcimer" is great. Somethings are quite easy, other stuff is quite difficult, but it gives a good indication of the variety of things you can do with a lap dulcimer.
If you can get this book, start with "Howie's Tune", which is really pretty and fairly straightforward. Sounds a lot harder than it is! Look out for records of Nicholson. Fantastic player.
Best of luck with it.