I've had to use to 3 times, sigh
and it has worked every time. It's a shame you can't buy the kit in the US but the method will work without it all you need is a good lice comb. This is long so bear with me....
1) Wet hair and apply lots and lots of conditioner, preferably one with good slip. This will make the hair easier to comb and also slows down the lice so they can't escape so easily. Detangle with a normal comb.
2) Take a lice comb and go over all the hair section by section several times. Rinse out the comb after each stroke to remove the critters. I keep a bowl of water at the side. This step takes some time!
This first session should remove all the adult lice so no new nits will be laid. But you may miss some of the smaller lice and there will still be un-hatched eggs in the hair. So you need to repeat the process every 3 days to ensure you remove all the lice before they are old enough to reproduce which they can do once they are about a week old.
The eggs take between 7-10 days to hatch so you need to keep this up for at least 11 days but 14 days is probably safer.
You can see that is working because the size and number of lice decreases each time you do it. It takes some patience from you and the child but it will work and no chemicals required!