If you are certain that you will be receiving an income tax refund (both federal and state, if applicable), then you do not need to request a formal extension.
It is something of a popular myth that there is a penalty involved for filing (late) a tax return where a refund is due to the taxpayer; that is simply not true. There is only a penalty imposed if the reverse is the case (i.e., taxpayer owes a liability).
Thus, it would be advisable for you to simply wait to file until your replacement W-2 arrives. But please do not file your return until you do have that document. Otherwise, filing a tax return without a W-2 raises a whole other set of issues. You can read more about those matters here, if you would like:
https://ttlc.intuit.com/questions/3170112-can-i-file-my-taxes-without-a-w2
Thank you for asking this important question.
