Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Troubleshooting; Confusion; Communication Breakdown
ATC Issue All Types; Aircraft Equipment Problem Critical
Air Traffic Control Provided Assistance; Flight Crew Diverted; Flight Crew Landed in Emergency Condition; Flight Crew Requested ATC Assistance / Clarification; General Evacuated; General Flight Cancelled / Delayed; General Maintenance Action
Aircraft; Human Factors
Upon completion of low approach to Runway XX at ZZZ we raised the gear and observed both Left and Right HYDR PRESS lights illuminate briefly and then lights went out.  I looked at HYD pressure gauge and it was at the top of the yellow arc but quickly rose back up into the green arc.  We initiated another Approach.  On final; flaps 20 and gear down was called for.  As the gear was in transit we saw each HYDR PRESS light illuminate alternately; approximately 3 times and then both lights illuminated steadily.  The gear indicators showed 3 green and flaps were at 20 degrees.  We completed the low approach but on climb-out agreed to leave the gear and flaps in their current position.  The HYD Pressure gauge was in the yellow arc and I turned on the electric HYD pump which brought pressure back up into the green arc; and then I turned the pump off.  Flight Inspection was terminated and we went to holding to run checklists.  We ran [Checklist 1]; HYDR PRESS LIGHTS; followed by [Checklist 2] HYDRAULIC SYSTEM FAILURE LANDING and reviewed [Checklist 3] PARTIAL FLAPS LANDING.  We then requested priority handling with ZZZ approach and held in their airspace in VFR conditions to burn fuel down to 2200 pounds.  We picked up IFR clearance to ZZZ1.  We told ZZZ to relay to ZZZZ TRACON that we would be landing at ZZZ1 Runway YYR.  ZZZZ TRACON suggested that we land ZZZ2; 10;007 ft.  I stated that we are a 'Priority Handling' and we will land on [Runway] YYR.  ZZZZ TRACON asked if we could accept Runway YZL; (with the flow) but winds were 020/11 kts.  I restated that we are a 'Priority Handling' and will land on [Runway] YYR.  We flew RNAV (GPS) Runway YYR approach.  Our landing weight was calculated at 17; 844 pounds; REF speed with partial flaps 20 at 142 kts.  We completed [Checklist 2] checklist and on short final turned on Hyd pump.  We touched down approximately 300 ft. before Aiming Point Markings.  Normal braking was not available; spoilers did not extend.  Emer Brake handle was deployed and aircraft stopped in 9;900 feet.  Tires did not blow and we were able to exit Runway YYR at Taxiway ZZ under ships power; shut down; and evacuate.  Hydraulic fluid was pouring out of the belly of the aircraft between the two main gear.
[Narrative added no additional information.]
Learjet 60 flight crew reported loss of hydraulic systems during precision approach evaluations and elected to request priority handling. Flight crew elected to divert and made a safe precautionary landing.