I used RadioShacks electronics / component cleaner. Spray one side of the bearing.. let soak in for 15sec. Spin at high speeds for 30 sec.
Repeat process once more. Then flip bearing over.. and repeat for that side. The stuff eats all the grime, and or passes it out of the bearing... and dries without any residue.
Most times, I wouldnt use a lubricant. Arcade trackballs in home setting probably will never see enough revs to warrant it.
However, Ive been thinking about this more. I would try F21 (Formula 21). It contains Urethane, and its slick as heck... and not easy to remove once on a surface. Urethane is impact tough and slick and smooth... its what they use for rollercoaster wheels.
Ive used F21 in replace of Wax on Pinball Playfields... and the result is night -vs- day. 20% ball speed increase.. no dirty flakes or wax & dirty ball-trails. Barely a sign of dirt, even after a month of constant Arcade abuse, in a busy mall. Previous clean & wax... used to be required once a week... and by 2nd week... the playfields would be coal miner black. Operated with F21 for over 2yrs, and no wear or problems. Cleaning was a cinch... a quick wipedown.