If you've got a standard plastic wheel that fits on a collared bolt, I'd suggest powdered graphite.

 

Or liquid teflon synthetic labeled safe for plastics.

 

Thanks guys. It's got the same sort of wheels most rotary mowers have...yes, they're plastic. It's making high pitched noise once in a while as it's pushed. Not so much lately since the humidity masks the issue.

@MasterMech...

Also, any other parts of the mower that should be lubrucated?

 

Other than the wheels, all other lubrication needs are usually internal to the engine/transmission. Sometimes the axle pivots (for adjusting the height) have grease fittings but that's pretty unusual these days.

As far as your squeaky wheels go, if they are just a plastic wheel, dry graphite is the way to go for sure. But many wheels have at least an Oilite bushing installed in the center if not a ballbearing. If that's the case, usually a thorough cleaning is all that's required as the bushing is already impregnated with oil.