I agree with OTW and Jill - a short handwritten note is the BEST thing to do! All you need to do is tell your sponsor is how much you appreciated the invitation and how much you enjoyed yourself and that it has further crystallized your desire to become a blah-blah-blah (I forget what symbols you are using). And be sure to end by saying that you look forward to the next opportunity to get involved. You could also re-state what you talked about at the other lunch you went to --e.g. your willingness to help if desired at any upcoming philanthropic events.... Just double check to make sure there are no spelling or grammar errors and it is legible!!!!
Sounds like it was a great afternoon!