For those who have had the ASSERTION FAILED error, try this.
I had to shut down Lightroom 5.5 abnormally (held down POWER button for 10 seconds) because Lightroom locked up my desktop. On reboot, everything came up fine but Lightroom gave the ASSERTION FAILED error. This is the first time I've ever seen this error so I went to new Adobe website for help. Don't bother, the site is useless and difficult to navigate. Secondly, I went to the web and it seemed that most articles pointed to a missing Pictures folder. Also not correct for me.
I could not get past the error, even reinstalling the software. I was about to re-install again from Lightroom 5.0 when I started looking at files and file locations. To make this short, I went into my Lightroom backups and used the catalogue from my last backup and Voila, Lightroom came up just fine.
My guess is that when I took the system down abnormally, I corrupted the catalogue and that caused the error. Try using a clean catalogue file as, for whatever reason, Lightroom might see your catalogue as corrupt. If you have don't have a backup (perhaps a new installation) but have a second machine with Lightroom, just export an empty catalogue to the machine where lightroom is not working and try to open it.
NOTE: during my testing, I could not open Lightroom to then open another catalogue. I had to find a catalogue (backups) and then double-click on the LRCAT file and let the file associations call up Lightroom. Once that was done, it was easy enough to make this my default catalogue.