Tech Specs;
1.1" LCD, backlight removed
4 white LEDs, total of 60(+/- 5) lumens
1.5" fresnel lens(credit card magnifier) before and after LCD, with 5mm between fresnel and LCD
No triplet/duplet yet
Form factor- roughly 4"x2"x1.5"(currently housed in small mint tin - handy, aren't they?)

The purpose of this project is to use a cheap picture viewer like this one and convert it into a projector.
I've tried using the main lens from a disposable camera(.5" dia), the convex/concave lens assembly from the same camera(.5" square), a toy telescope(.5" dia, much too convex),a small magnifying glass(.75" dia), and even a large magnifying glass(3" dia). I might try to use eyeglass lenses, maybe weak positives(+1.50) to try to construct a tiny duplet.
Every attempt I've made so far, besides the very first disposable camera lens, has been way too convex, so the image was extremely distorted.
I've spent the last week browsing(lurking) on these forums trying to read up on the relationship between screen size and triplet diameter, but I can't seem to find any direct correlation. Maybe I'm not looking hard enough. Does anyone know how I could calculate the size(diameter, focal length, etc) of the lens(es) needed? Or should I just experiment and hope for the best? I apologize in advance if I've overlooked an obvious thread.

This will be very intersting to follow.

I have tried to do a similar thing using a credit card fresnel and a jeweler's triplet magnifier. So far my LEDs havent been bright enough to get a decent picture.

My LEDs are easily bright enough:D 4 of them soldered to perf board, then placed inside an opaque tube and wrapped with electric tape, and to top it all off, a small magnifying lens that was frosted to act as a collimator. If you're having trouble finding bright enough LEDs, try looking at those little head/wrist work lamps at Wal-Mart. The one I pulled LEDs from had 12 of them arranged in an elipse, and one very bright one in the middle. The whole unit boasted 120 lumens.

i used a lens from the eye piece of binoculars - i completely demolished the binoculars just to get the lenses. Any who, I had a ipod mini video, I was able to to get a good sized picture with the single lens. though i could only get decent light from watching bright disney movies. I did not open up the ipod for this project. My point being, I just used what I had and got it to work. So, whatever works for you is the right thing. not sure of any formulas for lenses ect.

If you don't mind what type/size/lumes LED are you using?

here is a patent for a lense http://www.patentstorm.us/patents/7104672/description.html might some theory in there to help you.

Standard size 5mm round LEDs, taken from Black&Decker forehead mount worklight. Package said around 180 lumens for 12 LEDs, so math says 180lumens/12 LEDs=15 luymens each. 4 LEDs@15 lumens each= 60 lumens total.
If you're looking for high intensity LEDs, here is one on Digi-Key that is listed as 42000mcd, whereas on the datasheet is listed as 52 lumens(converters online said 36), 60* viewing angle, for $4.75 each. That's about the same price as a white LED at your local RadioShack! Not sure about how hot it might get though. Worth a look, even if you'd have to mount it to a heatsink.
Anyways.
I didn't even think of binoculaurs! Amazing what you'll overlook as potential lol. I'll definitely try that. Thanks.