When you're asking make it very clear what your intended use of the recordings would be, how you would store them and how long you'd plan to keep them.
Many lecturers may be reluctant if there's a chance you could upload their lectures without permission to youtube, share it with friends or use it to mock them in any way. Likewise if you can assure them that the recordings would be kept securely (password protection on any harddrives?) and would be destroyed (or sent to them and destroyed) once that module is complete then you're demonstrating an understanding of their privacy and intellectual property of their lectures.