I was able to get it working but gathering the individual mods and replacing the updated ones in the mods folder.
So to break it down:
1. Gather the mods. [[ http://www.fileswap.com/dl/Z4UmpaWhe/ ]]
2. Go to your mods folder for tekkitlite. [[ C:\Users\YOUR_USER_NAME_HERE\AppData\Roaming\.technic\tekkitlite\mods ]]
3. For each of the mods it says is missing, find them in the zip file and drag them into your mods folder. (I only rolled back the ones in the list)
4. Remove the newer version of each.
Just a heads up, so far I haven't had any problems but be aware that you'll be using an untested combination of mods and it could be unstable.
Also, I highly recommend backing up the tekkitlite folder before you make any changes. If something goes wrong, restore the whole tekkitlite folder.