G'day Scanman Dan,
You won't really find cutting tools much smaller than 8mm, I think I have seen 6mm in the past, but not very often.
If you need a really thin section to machine say, a groove into a piece of rod, this is a method I have used with great results....
Get on ebay and buy a selection of HSS blanks (4mm square). Then if you don't have a bench grinder or even a Dremel type rotary tool, go and buy a cheap set of grinding / cutting wheels and shanks from a hardware store, should be less than about $20 (get the ones designed for the Dremel type tool).
Attach a 'green' grinding wheel to one of the shanks and secure it in the chuck of the lathe, let it hang out a bit. Then secure the tool blank in the tool post at 90 degrees to the wheel. Start the lathe and slowly move the cross-slide past the grinding wheel (left and right), keep moving it in and repeating until you have ground a suitable angle on the front of the tool (there are numerous references to this on the web). To get a very thin section (say .5mm wide), move the cross-slide to the edge of the wheel and slowly crank it in so the wheel is grinding lengthways down the HSS blank. You don't need to go down far is you only need to make shallow cuts, keep repeating this process until you have ground enough away to get the desired sized tool.
Essentially this is using your lathe as a bench grinder, but by mounting the HSS blank in the tool post it give you much greater control of the cuts / grinding that is being done.
This is not an ideal setup, but has produced pretty good results for me when I have needed to machine very small grooves in alloy.
Don't worry about lack of skill, we all had to start somewhere, just keep having a go and you will work out how to overcome little hurdles like this.
If you don't have already, get yourself a proper parting off blade and holder, this will immediately allow you to make thin grooves in metal as they generally range in size from 1.5 to 2mm wide. You may not want the expense of a quick change tool post at this stage, but that would also be worth considering later.
You also need to spend some time planning how to cut the piece to minimise waste, and to make the operation easier.
Let me know if you need more info, happy to help.
Good luck.
Colin