Search the online FARs
To get the details of what the run-dry testing means, you can pull up the online FAR requirements and look at the guidance that explains how the test should be completed:
The 30-minute test is just a gearbox test that to demonstrate a standard of reliability an it is shown once before aircraft are certified. It does not imply that the aircraft can or should be flown for 30 minutes after loss of lube.
Here is the rule that the gearboxes are certified to:
From FAR 29.927
c) Lubrication system failure. For lubrication systems required for proper operation of rotor drive systems, the following apply:
(1) Category A. Unless such failures are extremely remote, it must be shown by test that any failure which results in loss of lubricant in any normal use lubrication system will not prevent continued safe operation, although not necessarily without damage, at a torque and rotational speed prescribed by the applicant for continued flight, for at least 30 minutes after perception by the flightcrew of the lubrication system failure or loss of lubricant.
(2) Category B. The requirements of Category A apply except that the rotor drive system need only be capable of operating under autorotative conditions for at least 15 minutes.
Here is the guidance material for this test (from AC-29)
(1) Section 29.927(c) prescribes a test which is intended to demonstrate that no hazardous failure or malfunction will occur in the event of a major rotor drive system lubrication failure. The lubrication failure should not impair the ability of the crew to continue safe operation of Category A rotorcraft for at least 30 minutes after perception of the failure by the flight crew. For Category B rotorcraft, safe operation under autorotative conditions should continue for at least 15 minutes. Near the completion of the lubrication failure test, an input torque should be applied for 15 seconds to simulate a minimum power landing following autorotation. Some damage to rotor drive system
components is acceptable after completion of the lubrication system testing. The lubrication system failure modes of interest are usually limited to failure of bearings, gears, splines, clutches, etc., of pressure lubricated transmissions and/or gearboxes. A bench test (transmission test rig) is commonly used to demonstrate compliance with this rule. Since this is a test of the capability of the residual oil in the transmission to provide limited lubrication, a critical entry condition for the test should be established. The
transmission lubricating oil should be drained while the transmission is operating at maximum normal speed and nominal cruise torque (reacted as appropriate at the main mast and tail rotor output quills). A vertical load should be applied at the mast, equal to the gross weight of the rotorcraft at 1g, and the lubricant should be at the maximum temperature limit. Upon illumination of the low oil pressure warning required by § 29.1305, reduce the input torque for Category A rotorcraft to the minimum torque necessary to sustain flight at the maximum gross weight and the most efficient flight conditions. To complete the test, apply an input torque to the transmission for approximately 25 seconds to simulate an autorotation. The last 10 seconds (of the 25 seconds) should be at the torque required for a minimum power landing. A successful demonstration may involve limited damage to the transmission, provided it is determined that the autorotative capabilities of the rotorcraft were not significantly impaired. For Category B rotorcraft, upon illumination of the low oil pressure warning light, reduce the input torque to simulate an autorotation and continue transmission operation for 15 minutes. To complete the test, apply an input torque to the transmission for approximately 15 seconds to simulate a minimum power landing. A successful demonstration may involve limited damage to the transmission provided it is determined that the autorotative capabilities of the rotorcraft were not significantly impaired. If compliance with Category A requirements is demonstrated, Category B requirements will have been met.