Propulsion system having fluidly separate lubrication systems for propulsors and turbo-engine

A propulsion system comprising:

• a turbine engine comprising:
• a turbo-engine including a low-pressure shaft and one or more engine bearings;
• a first propulsor having a first propulsor shaft;
• and
• a first gearbox assembly having a gear assembly, the first propulsor shaft being drivingly coupled to the low-pressure shaft through the gear assembly;
• a second propulsor that is remote from the turbine engine, the second propulsor including a second gearbox assembly having a gear assembly;
• and
• a lubrication system comprising:
• a first gearbox lubrication system disposed within the first gearbox assembly, the first gearbox lubrication system is configured to supply lubricant to the gear assembly of the first gearbox assembly;
• an engine lubrication system that is configured to supply lubricant to the one or more engine bearings, the first gearbox lubrication system being fluidly separate from the engine lubrication system;
• and
• a second gearbox lubrication system disposed within the second gearbox assembly, the second gearbox lubrication system being configured to supply lubricant to the gear assembly of the second gearbox assembly,
• wherein the first gearbox lubrication system is configured to supply the lubricant to the one or more engine bearings when the turbine engine is shut down.