Is it possible to run a 10.04 or 12.04 or earlier LTS containerized under LXC or Docker on Trusty?

You can run older Linux programs on newer kernels. Linux maintains backward compatibility (at least for all documented interfaces), for the benefit of people who are running old binaries for one reason or another (because they don't want to bother recompiling, because they've lost the source, because this is commercial software for which they don't have the source, etc.).

If you want to have a build environment with older development tools, or even a test environment for anything that doesn't dive deeply into kernel interfaces, then you don't need to run an older kernel, just an older userland environment. For this, you don't need anything complex: a chroot will do. Something more advanced like LXC, Docker, … can be useful if you want the older (or newer, for that matter) distribution to have its own network configuration. If you don't want that, you can use what Debian uses precisely to build software in a known environment (e.g. build software for Debian stable on a machine with a testing installation): schroot. See How do I run 32-bit programs on a 64-bit Debian/Ubuntu? for a guide on setting up an alternate installation of Debian or a derivative in a chroot.

If you want to run the older distribution's kernel, you'll need an actual virtual machine for that, such as KVM or VirtualBox. Linux-on-Linux virtualization with LXC or the like runs the same kernel throughout.

➜ codetv_static# docker run ubuntu:10.04 /bin/echo 'Howdy!' Unable to find image 'ubuntu:10.04' locally 10.04: Pulling from library/ubuntu a3ed95caeb02: Pull complete 86b54f4b6a4e: Pull complete Digest: sha256:f6695b2d24dd2e1da0a79fa72459e33505da79939c13ce50e90675c32988ab64 Status: Downloaded newer image for ubuntu:10.04 Howdy!