If you lose sys A after takeoff,the gear wont retract.
As latetonite wrote you 'need' nr1 engine to fail for the LGTU to operate.
The LGTU is for the gear to be retracted within 8 secs and the 2nd climb gradient not be delayed as engine 1 is operating sys A engine driven pump.
Both engines running and gear down wouldnt be an initial climb gradient issue.
The switching to ALT NWS on the ground would indeed activate the LGTU but i fail to see any operational reason unless you dispatch with the left engine out,an idea for Kramer i reckon
