I have a LRA tank & have had the same or very similar problem
My D4 stopped one day & had to call Land Rover Assist, what I had noticed since fitting the aux tank was every time I took the fuel cap off to fill it there was a significant vacuum release. Anyhow on the day the D4 stopped & would not start the LRA mechanic advised he thought it was a fuel supply problem, he then removed the fuel bleed cap & pushed the schroeder valve & low & behold it released fuel & air indicating it was out of fuel, the fuel gauge however was reading quarter full. At this point I did some figures on fuel economy & they were very impressive, I then went to the fuel filler & removed the cap, the usual extreme vacuum release occurred & the fuel gauge fell to empty!!!!.
I then pumped fuel from the aux tank & after some turning over it started & ran as normal, I think its a venting problem, I have since cleaned the fuel cap vent but havn't done any long trips since the problem occurred, I'm also going to check the tank vent lines to see if there is a problem (if it still vacuums), anyhow I hope this helps, pm me to discuss further & I'll give my mobile number.
Disco 4 2016 - ran out of fuel 3 times
Not quite.
The tank is a long tank running parallel to the DS of the vehicle.
The sensors are located fore and aft