What's the host & hypervisor? I do virtualization for a living, and short of architecture or endian issues, I have yet to see a 64-bit CPU that won't run 32-bit code (with the correct libraries of course); and that's talking Sparc, Power, and x86.
I run KVM on a Phenom II host with a 64-bit Kernel, 32-bit user land, and LMCE 32-bit running as a VM. Before anyone thinks I'm crazy (hmmm, maybe? ;-). The host OS started life as a 32-bit Debian 3 install on an over-clocked Pentium 233 MHz, and has been through a number of in-place OS and hardware upgrades over the years, now currently Debian 7.1. Multi-arch may let me finally go all 64-bit, or I may bite the bullet and re-install. So much to do, so little time...
FYI, there is no current 64-bit LMCE builds...
HTH!
/Mike