actually Marc. lime is acidic. thats how you get the cymbal to shine. is the same as cymbal cleaners. they are all solvents. so i wouldnt overdo it with the lime. it WILL remove surface metal as well. and be sure o clean off all residue. or the acid will eat into your cymbal.... dirt can be cleaned off without solvents. a good rub will do. Shine is only restored by removing a layer of surface metal that has oxidised and thus become blackish
lime is acidic, but its an organic acid - citric acid. its quite concentrated, seeing how its fresh from the source itself, but overall its still a better choice than cymbal polishers because the cymbal polishers polish and buff the cymbal. by buffing the cymbal, you effectively oxidise a thin layer, removing it to reveal the shiny untouched layer under it. whereas for lime, the acid isn't strong enough to completely oxide the top layer. further more you'll only leave the lime juice on it for a while before cleaning it off. overall its a cheaper alternative, and it definitely has less long term damage as compared to the other cymbal cleaners.
of course you gotta neutralise the citric acid by using shampoo, as marc mentioned in a few other posts, otherwise there might be residue citric acid left on the cymbal, and over time, it will still prove to be detrimental for your cymbal.
another point to note is that you do not have to regularly polish your cymbals - you'll do more harm than good. if you've got minmal stick marks, finger prints or dirt on it, warm water + mild soap will do. give it a good rub, dry it and it'll all come off. personally i don't like polishing my cymbals... i like the "aged" feel, and the worn in sound/feeling. alot of drummers argue that a "dirty" cymbal sounds warmer and more worn in... personally my ears aren't that kilat to note the diff lah, but i think its kinda cool to have dirty cymbals.
oh yes, and just a side note, clean your cymbals with a dry soft cloth after practices.. esp. if you have sweaty palms and you grab your cymbals ALOT. i found out the hard way when i first started playing cuz there was oxidation on my cymbals... was a bitch to remove and there're still small stubborn specks around on my ride.