Yes, most synthetic lubes do not need the LSD additive. Read the bottle carefully though to make sure.

If you are just topping off for a small amount of lost fluid, then there should be enough additive still in there. If it's more than about 1/2 quart needed, then I'd probably add it.

Also, some synthetic lubricant manufacturers recommend not mixing with melted dinosaurs (petroleum based). Read the bottle to make sure.