Laser, at this time, has never ever successfully had a trial where light hair was removed. No matter what anyone says. The minute it becomes feasible, the studies will be published, but so far there is no laser that can treat light hair. We have lots of companies here that say they can treat light hair (some of them dye the hair first and everything), but it’s all wishful thinking combined with a money-making mentality.
If your hair is fine, then it’s not good for laser either way, because laser needs to be used on COARSE hair only. It can induce growth on fine hair, especially female faces (the most common area for laser-induced growth). We have tons of posters on these forums who were told they could have lip/chin/cheek hair removed when it was really too fine or light, and now they have lots of new thick hair as a side effect. Laser is a serious technique and very useful, but only when used on appropriate areas, despite what many clinics say.
Also, shaving doesn’t make the hair thicker. That’s an old wive’s tale because people start shaving at puberty- Right around the time the hair thickens on it’s own due to hormones. In the olden days people thought the shaving caused it, but that was scientifically disproven quite a while back. Part of the reason it still persists is because the hair feels “pokey” when it’s been shaved since you make the tip blunt. The hair growth isn’t actually affected at all, it’s just an optical illusion.
My point is, bleaching is fine but don’t go around telling anyone that shaving made their hair coarser. Some mom’s do that to guilt their young daughters out of shaving, but hair is genetic and hormonal, not caused by shaving, and that misinformation just won’t die.
I think electrolysis would be pretty easy for you if the lip is the only area you want to do, as long as you get a good electrologist. Even if you only get a couple of clearances, the difference will be huge. 
Good luck, and let us know if you decide to go with electrolysis.
(P.S.- Vaniqua is so expensive, electrolysis would be cheaper, so I personally wouldn’t buy vaniqua. But it does work as long as you keep using it.)