At least a couple of months I'd expect, although it may never get that far because the union chose to decertify BEFORE the CBA expired and that provides for the league to employ the sham defense per the CBA:
Article LVII, Section 3(b) of the CBA, which states as follows: “The Parties agree that, after the expiration of the express term of this Agreement, in the event that at that time or any time thereafter a majority of players indicate that they wish to end the collective bargaining status of the NFLPA on or after expiration of this Agreement, the NFL and its Clubs and their respective heirs, executors, administrators, representatives, agents, successors and assigns waive any rights they may have to assert any antitrust labor exemption defense based upon any claim that the termination by the NFLPA of its status as a collective bargaining representative is Article LVII, Mutual Reservation of Rights: Labor Exemption or would be a sham, pretext, ineffective, requires additional steps, or has not in fact occurred.”
That being the case, an injunction against the lockout should not be granted.