I am having the same exact problem with Captivate CS5 - just upgraded to Lion 10.7.1 a few weeks ago. Today I discovered that I can't successfully record a project without the black screen. Even worse, the program will just crash before I can stop recording.
Did you figure it out?
Okay, this is what I've done. I pulled Captivate 5 off my Mac (OSX 10.7.1, MacBook Pro), then reinstalled. Tried to do a Record New Project, and the black background was gone. Published the project, worked just fine. Then upgraded to Cpativate 5.0.2...received an errror message on the install. Program still started up okay, but when I went to do a Record New Project, the black background had returned. Went back in, removed Captivate from the Mac, and reinstalled Captivate 5.0, without the update. Seems to work just fine. Again, probably some oddity in my system that will not allow me to use the 5.0.2 update, but it does seem to work okay with 5.0.