I think in this case, where the pullup resistor is providing the current to charge the gate capacitance far in excess of what the LS138 is providing, that the Gate (not Base) current limit resistor can be skipped.
I think in this case, where the pullup resistor is providing the current to charge the gate capacitance far in excess of what the LS138 is providing, that the Gate (not Base) current limit resistor can be skipped.