A patrol officer conducts a lawful traffic stop, and the driver does not have a valid drivers license. The driver is not the owner of the vehicle, and tells the officers that it belongs to the mother of his friend. The vehicle is impounded, and the driver refuses to leave the key to the vehicle. After the driver is released, and somehow the vehicle gets locked. The vehicle is impounded with no inventory. No other PC exists for a search warrant. Does the officer have the authority to enter that vehicle for an inventory?

Here's what Lafave has to say:

Inventories should not be upheld under Opperman and Bertine unless the government shows that there exists an established reasonable procedure for safeguarding impounded vehicles and their contents[FN81] and that the challenged police activity was essentially in conformance[FN82] with that procedure.

FN 82 ("If there is some deviation from the usual routine, there may be some justification because of unusual circumstances. See, e.g., United States v. Lomeli, 76 F.3d 146 (7th Cir.1996) (though police department's inventory policy calls for inventory of “vehicle prior to leaving it parked or removed from the scene,” inventory at station lawful here, as officer's delay “was based on concerns related to the purpose of an inventory search,” as he elected “not to conduct the inventory at night on a dimly lit street, but instead to conduct a thorough search at the station” where there was “enough light to search the car [without] missing some items in the car”); Black v. State, 418 So.2d 819 (Miss.1982) (inventory delay to following morning justified by fact emergency arose requiring all officers to spend time directing traffic); Rudd v. State, 649 P.2d 791 (Okl.Crim.App.1982) (8 hour inventory delay justified by extensive investigation at scene of accident).")

3 Search & Seizure § 7.4(a) (5th ed.); see also Barrett v. State, 718 S.W.2d 888, 891 (Tex.App. – Beaumont 1986, pet. ref'd) (one hour delay, though "not condone[d]", did not invalidate inventory search.)

So I think an inventory search at the impound lot would be ok if it was done promptly and there was a reason for the delay. United States v. Davis, No. 2:11CR30, 2011 WL 6152862, at *7 (N.D.W.Va. December 12, 2011)(search done the next morning at impound lot upheld in light of overtime policy etc.).
You should look at the inventory policy where the car was impounded.