Just run to the drug store and pick up a bottle of isopropyl alcohol, the higher the purity the better.
I have some thermal compound remover that I use from time to time. Each set comes with two bottles, one you apply and soak in first, and another you use for the final clean. I don't know if they're a rip-off, but they get the job done very nicely.
I don't think the lemon juice idea is a very good one though. You're going to get a lot of water and sugar everywhere. Lemon juice is mostly water and sugar. Besides, you still have to go out and buy the lemons or the bottle of juice. Might as well pick up the isopropyl and then you have something for cleaning your computer, and topically cleaning your wounds.
I think i'll probably go get some isopropyl alcohol or the propper stuff. I do have lemon juice in the fridge but I didn't much like the idea of putting it on my processor which is why I asked for your opinions. Doesn't look like any of you have even heard of it so it's probably not a common practice to use lemon juice to clean processors!!
I always use 91% isopropyll alcohol. I would not use lemon juice; even if the acidity cleaned off the old thermal paste, it would no doubt leave a residue. Lighter fluid also leaves a residue, as does WD-40; those things shouldn't be used.
After removing the old paste, apply a small rice-grain-sized dab of new paste to the top of your CPU, and use your finger in a plastic bag to spread it evenly over the surface.