Mint may be a bit heavy even with LXDE. Mint and Ubuntu include the stock
kernel with lots of drivers and codecs. Lubuntu will run on 128 MBs of RAM,
but it is recommended to have at least 256 MBs and that is what is required
for Mint LXDE. The big difference besides the RAM is that Mint LXDE tries
to look like Mint with Mint's slab menu (not a fan of slab menus) etc,
while Lubuntu uses LXDE with a theme. I would recommend stock LXDE for
anyone who likes old GNOME and Mint LXDE for anyone used to Mint, although
the extra 128 MBs of RAM needed for Mint may be the deciding factor.

Some distros are lighter wweight because they remove things from the kernel
and compile their own kernel. Crunchbang is a good lightweight distro.
Puppy is as well, although many find it hard to install on a HD for some
reason. SliTaz is a good choice. Tiny Core is the smallest user friendly
distro. Vector Linux (Slackware based) is great for older hardware. Unity
Linux (Mandriva based) is very user friendly. Damn Small Linux is no longer
in development, but was once the best. You can still find copies, but it
uses an old kernel and may not work with everything. I would avoid it.
Bodhi Linux is getting lots of kudos (have not tried it though). It is
Ubuntu based but uses Enlightenment and runs on 128 MBs of RAM. They cut
down the kernel and make it run faster than stock Ubuntu or Mint. Many
lightweight distros use OpenBox as their desktop and this gives basic
functionality but not much more.