Just for the record -- I tried the second way, which should be simpler, i.e. installing Debian and then converting it to LMDE.
Debian with encryption and LVM:http://forums.debian.net/viewtopic.php?f=10&t=46874
Conversion:http://www.khattam.info/howto-change-de ... 11-27.html
Either I am really stupid or this does not work.
a) after setting encrypted partition and on top of this, LVM initially Debian while booting tries to set up LVM, instead of dmcrypt (but from installation the dependency should be known), I don't know how this affect the rest of the process of starting the system
b) despite 3 hours installation, and enabling Desktop environment, none of WM/DM starts by default, and startx is not available
c) since system is working, I tried the conversion -- when I executed first command, update of the system, apt-get stopped working with error stating there is no signature for LinuxMint repo
So, for now I am stuck...