Need help understanding LCD Power Enable circuit
You're on the right track, but missing an important step or 2.  


Yes, when LCD_PWRE goes high, T3 turns on, but this is not to "create a path from the power pins to ground".
When T3 turns on, it sinks current through R6 and both legs of D1.
This in turn has the effect of pulling the voltage at the gates of FET1 &amp; FET2 down - which turns them on - they're P-channel FETs, so with their source pins held at the supply voltage , pulling their gates low turns them on.
D1's purpose becomes clearer when you consider the other components around the FETs.
Each one has a parallel R-C connected between source &amp; gate. When T3 turns on to pull the gate low, the C's will charge up, and when T3 turns off, the C's will each  discharge through the R next to it. But notice that although both resistors are 27k, C1 is 22uF while C2 is only 100nF - so C1 will obviously take much longer to discharge than C2.
The effect of this is to have FET1 remain on for a little while longer than FET2 when T3 turns off. (Why this should be necessary I couldn't guess).  
Transistors T1 and T2 are used as a voltage level-shifter so that the 3.3V control signal can switch the 28V backlight supply.
When LCD_BKL is high (3.3v) there is no voltage across the base-emitter junction of T2, therefore T2 stays off.  With T2 off, no current can flow through T1's base, so T1 stays off.
When LCD_BKL is pulled low, T2 turns on, allowing current through T1's base, so T1 turns on and supplies 28V to the backlight.