Is "Items with expired lot" exception in ASCP governed by Exception set?

Is there a way to limit the "Items with expired lot" messages to a certain time horizon? Can such a window be set on Exception Set that ASCP refers to, and throws exception only if within the set window? From my testing it looks like lot expiry exception is not governed by exception set. We are on unconstrained plan, but that should not make a difference I believe.

Let me give an example. Suppose item A1 has two lots. Lot L1 expires on D+20 and L2 on D+40. D being the plan anchor date, is there a way to limit the exception for L1 and not for L2?