You might get a few more opinions if you posted in the Thailand forum. I don't know of any liveaboards leaving from Ko Lipe. Most are from Phuket and usually go to the Similans/Richelieu, although there are some shorter trips that go to Phi Phi or other locations. I would ping StevenL in the Thailand forums as he has a ton of information on this. There are also a bunch of forum threads discussing liveaboards in that forum.
Since you're on a budget, I would suggest looking into the Manta Queens and the Pawara. Pawara isn't exactly low budget, but it's great value for money if your budget can fit it in. It also is pretty heavily booked far in advance. However, if The Junk actually looked reasonable to you, then you might want to look into the other luxury boats in the area, like Diva Andaman and Diverace E. There is an incredible amount of options in that area of the ocean.