The two main problems I ran into were 1) software support at the application layer, and 2) video driver support. There is a herculean effort on the part of package maintainers to build software for distros, and no one has been building 32 bit version of software for years, even if it is possible to build from source. There is only a very limited set of software you can use, even CLI software because so many things are built with 64 bit dependencies. Secondly, old video card drivers are being dropped from the kernel. This means all you have is basic VGA "safe-mode" level support, which isn't even fast enough to play an MPEG2. My final try was to install Debian 5, which was period correct and had support for my hardware, but the live CDs of the the time were not hybrid so the ISO could not boot from USB. I didn't have a burner so I finally gave up.
So I think these types of projects are fun for a proof of concept, but unfortunately are never going to give life to old computers.
My first thought: How about using a current computer to run qemu then mounting the Lenny iso as an image and installing to a qemu hard drive? Then dd the hard drive image to your 32bit target. (That might need access to a hard drive caddy depending on how you can boot the 32bit target machine, so a 'hardware regress' I suppose).
My second thought: If target machine is bootable from a more recent live linux, try a debootstrap install of a minimal Lenny with networking (assuming you can connect target machine to a network, I'm guessing with a cable rather than wifi). Reboot and install more software as required.