You can use Single Oil ( the lubricate for Sewing Machine). But don't put too much on it, just a touch will do. And basically, if you always remove the string after play. you dont need to use lubricant at all.
Make sure the yoyo is not under sunlight all day, too humid area, or play under rain, or walk the dog on the water.
When the yoyo become unresponsive (cannot come up), its time to change Friction Sticker. Come to me during the meeting and ask Edward or Me, and we'll teach you how to change the Friction Sticker.
Rgds,
Stuart.