Ouch... this is very sad to hear Comidt. I hope you can bring that poor diode back to life. :-[
I can suggest something the other guys haven't suggested yet. Use some play dough. The way I solder to some very fine and tiny points is to cover the area with play dough and then make a small hole with a fine tip. You can do this and make your hole just where the pin was originally. Make sure the play dough is nice and thick and somewhat caving in where you will solder. Make sure the hole is not too big, but not too small, and make sure the only part you can see through the hole is the black insulation around the original pin. Use a pair of helping hands and hold the new wire you want to solder in there in place. Make sure everything (wire and original pin) are both somewhat covered with solder flux to help you and the diode out. Don't use too much flux or you might end up having to heat up the LD far too much. Just enough to make the surfaces wet is perfect. Heat the solder you want to use and drop a small amount in there and then let it cool.
If you did this right and your play dough was shaped nicely, you would have a perfectly shaped solder joint. You can also drop the solder in (a very, very tiny amount), then heat up some solder on the wire and solder to the solder you just dropped in. That will help you make the point right on the can itself as fine as possible because the solder wouldn't have to grab onto the pin + the base. When you connect the pin to the other side, you will have a nice and tidy solder spot. Afterwards, you can then tear away the play dough and you have a perfect solder joint.
I would suggest keeping the solder from forming a thick blob. Try to make it as thin as possible and as straight as possible rather than a ball. When it forms a ball, there is a risk it might end up bending and touching the base of the diode. That is not bad, just very annoying. There will be an electric flow going through the line, but it will automatically be grounded so the diode will not lase.
Best of luck man and I hope the diode itself is still okay. If it had been twisted before it fell out, there is a risk that the fine wire inside the LD is pulled, and that would mean you have a perfect dye, and no connection to get to it. But let's hope that it's still intact :'(
GL;
DDL