I know I should update the database in my GPS, but nevertheless I'm wondering if i can use an expired IFR-certified GPS with an out-of-date database in lieu of DME
The answer would appear to be "Maybe", per the AIM (table 1-1-6): You are permitted to use an IFR-approved GPS "In Lieu of ADF and/or DME", however the footnote (3) to that table tells us that this use
Requires current database or verification that the procedure has not been amended since the expiration of the database.
So if you're using the GPS to calculate something like "5 Miles DME from JFK VOR" that would seem to be acceptable (the FAA is unlikely to pick up JFK VOR and move it without making a lot of noise about it), but if you're using by punching in a fix that's defined by DME and a radial you would need to somehow verify that the fix hadn't been redefined.
You can accomplish that verification in a number of ways (a current IFR chart on your iPad or a current paper chart seem like obvious ways). As long as you can satisfy yourself (and the FAA) that the data in the GPS is accurate the operation would appear to be permissible.
It would also appear that if you verify that the fix has been redefined (say FUBAR was 5 DME, now it's 6 DME) you could still use the GPS distance data in lieu of DME, just not the incorrectly-programmed fix. That is, you could determine when you're 6 miles DME from JFK VOR, and since you know the FAA didn't move the VOR and that the fix is now at 6 miles you now you're where you want to be.
I would argue that the answer is currently a definitive yes as long as you are not executing an approach or any published procedure including RNAV operations.
It's a case of permissibility by omission as no language exists which prohibits this operation.
The AIM contains this reference.
AIM 1-1-19f1(b) Equipment and Database Requirements - For IFR Operations "All approach procedures to be flown must be retrievable from the current airborne navigation database..."
RNAV operations are mentioned in AC 90-100.
AC 90-100, U.S. TERMINAL AND EN ROUTE AREA NAVIGATION (RNAV) OPERATIONS, paragraph 8a(3): The onboard navigation data must be current and appropriate for the region of intended operation and must include the navigation aids, waypoints, and relevant coded terminal airspace procedures for the departure, arrival, and alternate airfields.
I also found it interesting as I was renewing my CFI certificate that my training course made this assertion, but provided no citation.
Although you can fly en route IFR with an expired database, approaches are not authorized.
It's also interesting to note that Garmin says you can still file
/G with an expired database.
You may file your flight plan as /G if your 400W-series unit is an authorized IFR installation. The 400W series is a TSO C146a Gamma-3 (Class 3) authorized GPS navigator. If you are flying en route, you may file /G with an expired database only after you have verified all route waypoints. Approaches may not be flown with an expired database. See your approved Airplane Flight Manual Supplement for more information.
IFR Refresher also agrees.
While it is not legal for approaches, you can use an expired database for en route and terminal operations, as long as you verify the data is still correct, generally by reference to paper charts.
The question of whether or not GPS can be used in lieu of DME has been answered. Combining the two I draw the conclusion that the answer is yes.