Not really. This is a user-to-user forum. If you registered your original Lightroom with Adobe you can get the serial number from your Adobe account.
How did you come to lose it??
My computer had a virus. The hard drive had to be scrubbed. When I went to reinstall Lightroom I what I thought was the key code but after downloading onto the computer when I went to open the program it also wanted my original code along with the upgraded one. Now I don't know how to find the original.