Do you need to lubricate gears after cleaning gears and chain? I just cleaned my gears and chain with a biodegradable degreaser. I'm going to lubricate my chain. Do I also need to lubricate the gears or do I just pedal and make sure that I hit all gears? Will the lube on the chain lube the gears?

You don't need to lubricate your gears since they don't have any moving parts or pivots (it's the hub that rotates). Cleaning them is all you needed to do.