No, I won't fix your Lomo for you, I'd love to, but I have too much to do.
If you are the least bit squeamish about small fiddly things, stop reading right now. If you are the the kind of person who watches surgery on TV and thinks "how hard could that be?", carry on.
Ok, lets get started. I have succesfully brought my Lomo LCA back from the dead twice. The first time is a bit of a mystery, and I'm not sure if what I did actually fixed the problem or not. All I know is that it didn't work, and then it did. I'd like to think that I had something to do with that.
Symptom: Lomo makes familiar double click, film winds on normally, no pictures. I opened the back, and saw that despite everthing being apparently normal, the shutter was not opening. First, I changed the batteries, this did not help. Removed the bottom from the camera, and observed the mechanism from the bottom. At this point I connected a lab power supply to the points marked "+" and "-" on the photo, set the supply for 4.5 volts and operated the shutter. Initially I only did this to see if I could measure the current the camera was drawing, but it wound up solving the problem. Maybe. I'm guessing that part of the shutter mechanism was frozen, and needed slightly more current to free it than the batteries could deliver. If you try this, make sure your power supply is accurate! Little houshold adaptors are notorious for having voltages higher than that printed on them. I would try this with 3 D-cells in series if I didn't have access to a good adjustable supply. Also, make sure you have the polarity correct!
Symptom: Lomo makes single click, second click never comes, film will not wind on. Camera is completely jammed. Uh oh. first, rewind the film and take it out. Then, remove the three screws holding the bottom. One screw is longer than the others, it goes at spot "L". Remove the bottom, and note that catch "A" is holding wheel "C" from turning. (the picture is taken with catch "A" released normally, the film is ready to wind. Carefully pull back catch "A" (use a toothpick or something, I use dental tools for this kind of thing) and gently attempt to turn the film winder, when it starts to turn, release catch "A" and continue winding until "A" engages normally. Fire the shutter and observe linkage "B". (you must have batteries in place and lens cover open) It should move quickly to the left (if the camera is oriented as shown) and release catch "A". If it doesn't, gently push it to the left until it is in the proper position. You may hear a "click" as this happens. Once "A" is released, try to wind and fire again. At this point, things should be back to normal. If "B" is moving sluggishly, your camera needs to be cleaned and lubricated. That's beyond the scope of this page. (read: when I have to do it to mine, I'll show you how, until then I'm not touching anything in there!)
A few final notes: first, NEVER oil a camera unless you know exactly what you are doing, and have the correct lubricants. 3-in-1 or WD40 have no place in your Lomo! Second, have the proper sized tools- a good set of precision scewdrivers is worth its weight in gold. Cheap tools are worse than useless. I use Wiha brand drivers. You should check out the books by Thomas Tomosy (Camera Maintenance and repair, books 1 and 2), these are easy to get and excellent. I have a book on Russian camera repair by Isaak S. Maizenberg that is very interesting, it doesn't cover the Lomo, but there are lots of mechanical examples in it. It appears to be self-published and is probably impossible to find. I hope this page is of use to someone out there, let me know if you are successful