Device for writing a lecture with a stylus for video lecture recording
If your department has a document camera, especially a newer model, then you could use that. I currently use a document camera for my regular lectures. I write on the paper under the camera, the camera sends it to the computer and the computer sends it to a projector, where it gets projected onto the big screen in the lecture hall. This way I can look at my class the class the entire time and I do not have to worry about whether students in the back can read the writing on the whiteboard in front. 

The document camera I use can also be set up to display the images it captures on the computer. Then, with video capture software, (CamStudio is an example of one with a free option), you could record a video as you write.

If your department does not have a document camera, you can set up something similar with a webcam, which would be cheaper to buy but produces lower video quality. Set it to look down on the paper. You write your lecture, and the computer records it. Alternatively, your institution may have an instructional technology office that could loan you a document camera (or may even have a more advanced set up).