As Rushton said, the Magic Eraser + a dry stylus brush work better than most liquid cleaners (I haven't tried the Lyra liquid, but I abandoned two other liquids and two gel type cleaners long ago).
The only thing that works better IME is a sliver of ultrafine sandpaper, as Linn supplies, but I've only needed that to rehabilitate neglected styli sent to me by friends or dealers. Regular use of the ME + brush is sufficient to prevent any buildup.
Caution: I've received correspondence from dozens (hundreds?) of audiophiles since introducing the Magic Eraser-as-stylus-cleaner four years ago. Only three of them ever experienced a problem with any stylus cleaner, and ALL THREE WERE LYRA OWNERS. Two Magic Eraser users and one Lyra liquid stylus cleaner user had their styli fall off the cantilever during cleaning. (!) From this, the prudent conclusion is that Lyra's method for affixing stylus to cantilever is (or was) less secure than most. Whatever stylus cleaner you use, proceed with care.