LCOE refers to the price in MWh (produced electricity), so it takes capacity factor into account. Whatever electricity you produce and sell depends on your installed capacity multiplied with the capacity factor.

Similarly, you pay for the electricity you receive and this is priced as say 40$ per MWh. Obviously when you receive nothing the price is 0, you don't pay them to idle, they either produce or not. Thus when storage costs kick in you don't add the costs of both together. You either pay one or the other, not both.

You might average them out taking into consideration what their output is, but you don't stack the costs on top of each other which I often see people do.