The best you can hope for is a dim image. The worst is a blurry, distorted, poorly focused, color-fringed, dim image.
It is certainly theoretically possible to focus the output of a TV through a lens to project an image on a screen. That's just basic optics, and how most of the large screen TVs work. However, the fundamental problem with this scheme is the limited brightness of a conventional television tube.
When you take a 20" TV and expand its image to 150", you are magnifying by 7.5x on the diagonal. That is approximately a 50x increase in area. With 1/50'th the light per square inch, the picture will be only 1/50'th as bright as normal. And that isn't counting all the losses through the lens and the reflecting screen. Guesstimate 50% losses (mostly in reflectance from the wall) and the picture is only 1/100'th as bright.
Will an image 1/100'th as bright as normal be usable? In a dark room it should be visible, although not with vibrance. Expect it to look dim and washed out. In a brightly lit room with windows open to the sun as shown in this "artist's rendition" from www.books4you.addr.com
Not a chance! These jokers ought to be paying fines for false advertising (they have some other doozies on their site as well).
Okay, let's say you can live with a dim image. What about the quality of that image aside from its brightness? If the lens they provide you isn't high quality, then you will suffer from all the other defects I listed earlier: general blurriness, visible distortion (e.g. straight lines are curved), poor focus (e.g. you can focus the center or the edges, but not both) and color-fringing. Now ask yourself why cameras and real projectors (both TV and film) have computer optimized, multi-element, anti-reflection coated lenses ground to precise concave/convex shapes from optical quality glass instead of a single Fresnel lens, and then further consider how much quality a $15 pressed plastic variant of a Fresnel lens can have...
Oh, one more thing. If they only use one lens in their projector plans (which I can't say for certain since they don't reveal their plans, but which I suspect from looking at the pictures and reading some of the text), then the image will be upside-down and reversed left to right. There are two ways to fix this: stand on your head while viewing or flip the television upside-down. Flipping your television isn't very convenient, but it is probably better than standing on your head for most people. However, the subsequent build-up of heat inside the cabinet doesn't bode well for the long-term health of your television (particularly if you have the brightness cranked up in an effort to compensate for the dimness of the magnified image). There is a reason for all those slots on the top of your television cabinet...
All in all, these plans are nothing but schemes to separate you from your hard earned money. They supply you with a product that is just barely functional enough to keep them from going to jail for fraud, but not something that you will be happy with. Save your time and money for something better. Of course, if you have already purchased a kit, don't fret. That Fresnel lens might not make a good projection TV, but it makes a heck of a good magnifying glass for frying ants
on a hot summer day...