I installed MEPIS on my laptop, very exiting about it, I think it is better than Kubuntu.
Then I tried to install my favorite editor LyX. It works but the system automatically installed an older version 1.3.7. I really want it to be a higher version 1.4.4.

Can anybody help me with it?

Here is the output of apt-cache policy lyx:

lyx:
Installed: 1.3.7-0ubuntu4
Candidate: 1.3.7-0ubuntu4
Version table:
*** 1.3.7-0ubuntu4 0
800 ttp://archive.ubuntu.com dapper/universe Packages
100 /var/lib/dpkg/status

It's installing the latest version available at the package reposity it uses (seems like it uses Ubuntu's reposities, and old ones -- Dapper was the Ubuntu version before Edgy, which will in 4 days become second-newest as Feisty is released). To install a more recent version you'll either need to configure the package reposities to be newer ones, if Mepis works fine with it (if it's not recommended by Mepis maintainers, it might not be wise), or hunt the .deb package of the newer version yourself. It's lyx-something.deb, and something depends on the version. After you've downloaded the file you can try to install it with
and if all dependencies are met, it gets installed. If the package depends on some other, possibly newer packages, you are informed (and then you'll need to find and download and install them first; this is why you usually use package manager like apt).