What does "max" really mean in gate trigger threshold of a triac?
It means that at the moment of trigger, when you are forcing just enough current into the gate to guarantee triggering of the thyristor , the gate voltage will be no higher than 1.3V (at 25°C). 

It may be higher at lower temperature, and it may be higher if you force more current into the gate. 

So, suppose you have a +5V supply that yields minimum 4.5V after a transistor switch drop and tolerance, you can calculate the required gate current-limiting resistor from Rgt = (4.5-1.3V)/Igt







simulate this circuit &ndash; Schematic created using CircuitLab

In the circuit above, I am showing the gate driven with negative current since the standard triac is not guaranteed to turn on in Quadrant-IV. 

Note that at low temperatures, the triac will generally be less sensitive than at 25°C and the gate voltage will also be higher, so to guarantee triggering at low temperatures you need to either put more current in at 25°C than would otherwise be necessary (the usual method) or make the gate current temperature sensitive with a PTC or something like that (rare).