OK, so first of all, what is a lap loom in the most basic sense? It's literally just a rectangular frame where you can tie warp strings on to! So don't feel like you need a fancy expensive loom, especially if you're just starting out. (The one advantage of those fancy looms is that they often come with a heddle bar which can help pass your weft threads through faster, but don't worry about that just yet.)
There are a few resourceful ways that you can put together a quick, inexpensive loom:
1. Go to your local thrift store and find the cheapest art you can find that is mounted on a sturdy wooden frame and is the size you desire. Strip the art off, and use some finishing nails to nail in. (See below to 3a. to see what nails I use.)
2. Go to an art store and buy stretcher bars that you can put together and use as the frame.
3. Have some tools and wood laying around? Make one yourself!