LL uses Xfce desktop and is based on Ubuntu 12.04, so according to that site it should be compatible. But, as I said, I haven't tested that myself -- so can't be 100% sure. (A different distro that I also use happens to have that feature built-in and it does work -- so my best guess is that it will also work if added to LL.)
I can tell you that using the second option on that page (Arandr) almost certainly will work. Before upgrading the distro version mentioned above, Arandr is what I used to get the multiple screens set-up properly on one of my computers. Also, I set up a friend's laptop for the same purpose as you (hooking up a TV screen to a laptop) using Arandr. Since she doesn't always have the laptop connected to the TV, I didn't put the script in the "Session and Startup" menu for auto-starting on every bootup. Instead, I just put a link to the script on the desktop. When she connects the computer to the TV, she just double-clicks the link and it activates the script to set-up the TV screen.