Chainsaw lubricant is pretty cheap, about the same price for 1/2 a litre as for a small bottle of bicycle chain lube.

My understanding is that grease is for bearings (hubs, BB, headset) and miscelaneous jobs like stopping bolts from seizing; oil (or wax or dedicated chain lubes) for the chain; and for cables, not sure what to think as I've heard so many conflicting opinions.