Both approaches lead to the fact, that Lightroom can start without crashing, but with error 213:10. I guess this is because Lightroom checks the modules loaded and builds a checksum, which after renaming the directories or launching it from a different location, will not match.
The answer is simple. You cannot install Lightroom on a case-sensitive file system disk. You can use a case-sensitive formatted external disk to store your photos, but the application itself needs to be installed on a standard (i.e. case-insensitive) file system disk.
Yepp, simple answer. Until 5.6 it worked. Seems that only the asneu.framework was introduced and the case sensistive writing has always been wrong, but still it worked on case insensitive file systems. As said, it starts but brings the licensing error 213:10, which might be a checksum.
I by the way also created a partition which is case insenstive and installed it with 'sudo installer -verbose -pkg "Adobe Photoshop Lightroom 5.pkg" -target /Volumes/insensitive'. Installation was fine, but licensing error still occurs.
I guess Lightroom is really creating a checksum over loaded modules with case sensitve file and absolute file names. That's why running it from /Volume/insensitive/Applications/Adobe Photoshop Lightroom won't work either, even on a case insenstive file system.