L IDG failed synoptic, from FlightSafety G450 Pilot Training Manual, figure 2-52, sheet 1.
I've never seen a generator on this airplane exceed 30% in normal conditions which tells me one generator should be able to power everything. That being said you will be vulnerable to losing the remaining generator.
If you have an airplane that allows inflight use of the APU in this situation, descending and firing it up should be a no brainer. If you need the gas and can't descend, you are going to have to do without the hot coffee.
But what about oceanic operations? If you lose the remaining generator you will end up on the HMG which means you are going to need that APU eventually and all that is going to complicate matters, isn't it? If it were me, I would be planning on the descent to 37,000' before I find myself without the 40 kVAs. If you look at your fuel charts, the penalty for descending from the forties to 37,000' isn't that bad.
What follows comes from the references shown below. Where I think it helpful, I've added my own comments in blue.
You have the following CAS:
AC Power Fail, L-R
The synoptics should show the affected generator in amber but the other IDG should pick up the load. In flight the only other evidence should be loss of power to the galley and perhaps the cabin, depending on outfitter options.
[G450 Aircraft Operating Manual § 2A-24-20 ¶2.C.]
[G450 Maintenance Manual, §24-25-01 ¶2.A.] The GCU can be reset from a fail-safe condition when power is removed from the GCU or when the left/right generator control switch is operated from off to on. This reset causes the software to re-initialize. If the conditions that caused the microprocessor fail-safe are still present, the microprocessor will fail-safe again.
More about this: G450 Systems / Electrical Control Systems / GCUs.
[G450 Airplane Flight Manual, page 03-04-10]
With one (1) generator inoperative, monitor and limit loads to less than 100% AC. Accomplish this by switching off equipment as necessary.
This resets the GCU
This permits restoring the generator to the bus.
If proper power is produced, automatic bus transfer back to the normal configuration will occur.
If above 37,000 ft, consider descending to APU starting altitude to supplement operating generator.
If both generators fail, see Dual Generator Failure.
FSI G450 PTM, FlightSafety International Gulfstream G450 Pilot Training Manual, Volume 2, Aircraft Systems, October 2008
FSI G450 MTM, FlightSafety International Gulfstream G450 Maintenance Training Manual, August 2008
Gulfstream G450 Aircraft Operating Manual, Revision 35, April 30, 2013.
Gulfstream G450 Airplane Flight Manual, Revision 36, December 5, 2013
Gulfstream G450 Maintenance Manual, Revision 18, Dec 12, 2013