Finally, I resolved this one: the power tailgate on the LC300 has two finger entrapment pressure strips on the side of the tailgate itself. They plug in behind the plastic trim attached to the inside of the tailgate. You can only access these plugs by dropping down the internal trim mounted to the inside of the tailgate. They are not accessible through the switch holes or blanking plate hole on the edge of the tailgate.
I have found in research that some of these edges fail within the first few days of buying the car.
One of edges was faulty.
If when you press any close button (front, rear or remote keyfob) and hear two beeps, one of both pressure strips is activated, and therefore the tailgate will not close. It's a safety device to reduce the risk of getting trapped in the tailgate.
These types of pressure-sensitive strips are used extensively on UK machinery and are generally unreliable from my experience.
If you press any close button (front, rear or remote keyfob) and hear a long constant beep, it indicates the pressure strips are not connected, ie unplugged or there is a cable fault.
A continuous beep beep beep indicates the tailgate is traveling, and is the normal safety warning for normal operation.
The pressure-sensitive strips are fully monitored on each side and use a 4K7 resistive circuit to detect faults. So if you want to prove one is at fault, if you place a 4k7 resistor across the connections on the tailgate having already disconnected the cable to the pressure switch which is normally plugged into it, the tailgate should travel. If not plug it back in and try the opposite side.
I have attached a photo of the pressure-sensitive strip which I have removed and left hanging on its cable so its easy to identify. I have also attached a photo of one of the receiver connector plugs inside the rear tailgate.