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Initially
it’s
used
to
determine
the
order
of
firing
(4)
Initially it’s used to determine the order of firing (4)
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The whole clue is the definition (& lit or double definition).
How the clue works
The whole clue is a cryptic definition of Initially it's used to determine the order of firing, LIFO standing for Last In, First Out — the principle where the last person hired is the first to be fired. The word "Initially" hints that the answer is an initialism made from the first letters of that phrase.