I'm facing the same issue. The Creative Cloud App needs some serious work.
With the last update, I had to uninstall and reinstall Lightroom to deal with the bugs, which I did through Creative Cloud. Yesterday, it showed my two versions of Photoshop, Bridge and Lightroom installed and up to date.
Today (after the update to the creative cloud app), I show updates available for both Photoshops, and Bridge, and I'm offered the option to install Lightroom. Yet when I start Lightroom (which definitely was installed from the cloud, not stand-alone), Lightroom offers me the option to update to v. 5.6, just as would have before creative cloud was initiated. (I have the Photography package.)
I think I'll just re-install Lightroom from the cloud, and see what happens.
How did you get on.
The install of Lightroom from the Cloud seemed to go just fine. All seems to be working as it should. But I saw the same behavior on my laptop: previous version of lightroom installed from the cloud, when update becomes available, Creative Cloud app shows lightroom as uninstalled, even thought it is working fine. Simply doing the install of the new version from the Cloud went fine, and the previous version didn't have to be un-installed.
I just don't get why the app doesn't seem to know that Lightroom is installed, once an update is released. Photoshop and Bridge show updates available, as they should, on the same machines. Not Lightroom. I guess it might be connected to the fact that Lightroom can still be installed without the cloud.