Yeah, wash your hands before playing!
Seriously, are you talking about the fretboard, or the actual neck itself? If it's your hands sweating a lot, you could try something like washing your hands before playing and maybe putting talcum powder on your hands. I'm not trying to say you have sweaty hands, but maybe you do - I know I have!
Don't use lemon oil ! it is great for a dry fretboard, but if yours is already oily why add more oil ???? I use what Dan Erlewine reccomends for stubborn grime; pure NAPTHA (lighter fluid). You can buy it anywhere that sells tobacco supplies. It won't harm your finish and it leaves things clean and dry. Get your cleaning cloth damp (not wet) with it and give it a good scrubbing. If it is caked on grime on your FRETBOARD, and it is rosewood, you could also scrub it with some 0000 steel wool.
Lighter fluid and a rag.
Its works like a charm.