That's because Lightroom is a little bit of an orphaned product. Even though Adobe strangely put Photoshop in the Lightroom name (I still don't understand that), they have nothing to do with each other. Lightroom does not use the activation of CS products at all and so it will not show up anywhere. This also means that you don't have to deactivate a license on a computer if you want to move to another machine or OS. Your license code will keep working.
Great it also means that when you call Adobe technical support, they won't speak to you, as I have already found out.
Unfortunately my Lightroom CD is kept by the IT department (let's just say bankers would be jealous of their hours) and that is the only place the serial number appears, since Adobe decided unwisely to remove it from the Help> About> screen. Guess I'll have to get the CD back and write down the serial number.
The tech support guy never bothered to tell me that it wasn't going to show up in my registered products list.
Best part, as has already been mentioned in the forum, customer service offered to sell me a manual! WTF?
Lightroom is seriously making me wonder about Adobe's commitment to its customers. I"ve been using Adobe Photoshop since 1994, back when it was on a Solaris box, and Adobe Illustrator since 1996. I bought Lightroom based on a friend's recommendation and my past experience with Adobe products. I'm disappointed.
WOW... I mean really, wow is all I can say.
I was on the phone with tech support asking if there was any other way to find my serial number since it didn't appear in the usual place of Help> About>. Because he wouldn't talk to me without the serial number. He told me Adobe had intentionally removed it from the software based on customer requests/complaints and it was only on the CD box. He also managed to imply his belief I had a pirate copy of Lightroom.
Yet there is is just like you said in system info... (why did Adobe move it?)
I guess the tech support guy just didn't want to work that day.
My disappointment in Adobe is doubled...
I had a problem in the past with my Adobe registrations. It began either with PSCS2 or PSCS3 ... can't remember which.
Back in the olden days you could choose you your own Adobe ID user name. All of my registrations appeared under this account as I added them myself when I purchased software. With the introduction of the later CS apps ... there is the function to register the software automatically during the installation process .. so I did ... what happened though, was either through my lack of attention or by default a new Adobe account was created using my email address as the Adobe login username ... after much frustration of seeking out why my serial numbers were not showing up in my traditional account, I discovered the existence of the second account by reviewing the confirmation email from Adobe for the new account ....
So ... at this point all my legacy software was registered under the old account, PSCS3, IDCS3 and Lightroom were under the new account ... all properly registered .. just in two locations ... so then I spent some quality time on the phone with Adobe CS and several hours later all my registrations appeared in one location and the extra account was deleted.
I don't know if this will help your situation ... just sharing my experience to see if it sheds any light on your situation ....
Once upon a time Adobe tech support was very good and knew the product.
There was no reason to move the serial number out of the about box. Worse though the tech support person I spoke with has absolutely no excuse for not directing me to the serial number so I could continue with my tech support call.
I noticed a similar issue to the one Butch expressed, my older products do not show up in my registered products list. Though I am sure at one time several of them did. I know for a fact Adobe Illustrator 9 and Photoshop 5.5 were there at one time, that was when I first started using the forums here. I wonder if they roll off old registrations?