Thank you very much for your prompt response and suggestion.
The setup over here is also via an autosave mechanism, since the files are fairly large (5 min imaging -> 20 GB). Thus, all I get are ".lof" and ".xlef".
I then installed the free version of LAS X from Leica (http://www.leica-microsystems.com/products/microscope-software/details/product/leica-las-x-ls/). As you mentioned and as far as I know, this is currently the only available program that can read these cryptic ".lof" and ".xlef" files!
It turned out, however, that LAS X could not convert the file, around 400 GB, from ".xlef" to ".lif" because there was insufficient disk space on "C" [around 250 GB]. By default, LAS X is using a "Temp" directory on "C". For large files this needs to be changed in "Configuration -> Memory Management -> Data Container Settings -> Folder on local Hard Disk" to something where there is sufficient space, e.g. "D". - Perhaps this is helpful to others.
Also, I submitted a request to the Bio-Formats Forum and in the hope support for ".xlef" and ".lof" files will soon be implemented in Fiji.
Do you have a script or something similar for batch-converting .xlef files in .lif files? Or do you load them individually into LAS X and then convert one by one?
Thanks a lot!