It's possible at the level of the packaging tools (apt). But the resulting system may not be equivalent to doing a reinstall, and you may get errors along the way. This is because many packages contain specific support for upgrades (e.g. handling changes in configuration files) but not for downgrades.
Normally, apt prefers to install the most recent version of a package. But you can change this through pinning: you can declare that packages from the old release have higher priority than the installed packages, so that they will be downgrades when you do aptitude dist-upgrade.
Change your /etc/apt/sources.list to include only the old release (either edit the file or use your favorite GUI), and run aptitude update. Then edit /etc/apt/preferences (documented in the apt_preferences man page) and add the following lines (to downgrade to lucid):
Package: *
Pin: release v=10.04
Pin-Priority: 1001
Then run aptitude dist-upgrade. Every package has a priority greater than 1000, so every package that is present in 10.04 and installed on your system will be downgraded. You'll have to remove packages that weren't in 10.04 manually; they'll be listed under “Obsolete and locally created packages” in aptitude.