Hey Lads, I'm an automotive tech and I do most of the wiring at my shop, so I'll do the best I can to help you diagnose this. First thing is a wiring diagram, i was able to track down one for a k2 gsxr1000 ( if anyone has one for this 600 it'd be better) but i am goin to presume the lighting circuit works the same. Next is a test light (probe that connects to either battery terminal and has a light to show when you have power), they make things go a lot easier in wiring, they are usually fairly cheap at the local parts stores.
Start with seeing where you lose power to the low beam in easy to access places, such as connectors or fuses.
Now you have checked the fuses to make sure they're not blown, so now use the test light to make sure you are getting power to them. With all connectors hooked up, the key turn to the on position and lowbeam selected, connect the test light to the negative battery terminal (this checks for power to where ever you probe), and touch both sides of the top of the lowbeam fuse with the probe. If the light on the test light lights up, you're good up to this point, if it doesn't you have a problem within the wiring system up to the fuse. If only one side of the fuse lights up but the other does not, the fuse is the problem ( even if it looks okay), change it.
Now use this to start, and if you feel up to it, check the rest of the system using the test light. My k3 is in pieces since its the off season here in Canada so i will put it back together and look at the system myself to see if i notice any other good connection spots to check.
Get back to me and we'll continue on from there.
Cheers