LIFO reserve itself is added to the inventory under LIFO in order to get the inventory under FIFO.
The change in LIFO reserve is added to the COGS under FIFO in order to get the COGS under LIFO.
So we can conclude:
Inventory under LIFO < Inventory under FIFO
COGS under LIFO > COGS under FIFO
Since inventory is an accumulated account (Balance sheet) and the LIFO reserve is the accumulated difference between inventory under FIFO and LIFO, then in order to calculate inventory under FIFO you add the LIFO reserve to the inventory under LIFO.
COGS is a flow, is the cost of goods sold in a certain period (a day, a month, a year), so you can’t add an accumulated account to a flow account right? Easy to remember: Income Statement accounts are flows, so need to add the variation, not the stock.
Hope this helps!