In regards to lubrication the short answer is: if the engines running the the gears are oiled.
Long answer below:
The clutches are actuated hydraulically. Unlike standard manual transmissions, a DSG-transmission has its own oil pump. On picture 7, the pump and its driveshaft are visible. The shaft runs through both main shafts into the clutch housing. When the engine runs, the oil pump is running and oil pressure is present.
The oil that runs through the oil pump is being used for several purposes:
Lubrication of the gears, shafts, bearings and clutches
Cooling of the transmission
Actuation of the gearshift mechanism
Actuation of the clutches
But I will add that the pump is fixed displacement and will have more flow the faster the engine turns. So if you put it in neutral the gears being connected to the road via the diff will be spinning at a higher road speed compared to the pump spinning at the same rpm as the engine at idle. where as if the engine and gears are both matched to road speed the pump will be flowing at the desired road rate. So take that as you wish
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