Do I need additional power for an IR LED diode 50 feet away from a Raspberry Pi?
TX IR LED 
Working Voltage : 0.9 - 1.3V
Reverse Voltage : 5V
Forward DC      : 30mA

You can drive an IR LED with higher current pulses (more than 30mA) as long as the maximum average current spec is not exceeded.

If you power the LED from 3.3V using a BJT (0.1V Vcesat) and a resistor to limit current, there will be 0.9-1.3V on the LED, and 1.6V minimum on the resistor. This is enough voltage drop to control LED current properly. For 30mA that would be a 56 ohms resistor.

Let's try 25AWG telephone cable. That's about 650 ohms/km. Two 20ft wires make 60ft so about 20m or about 13 ohms. At 30mA current that's 0.39V, it is okay. You can also measure cable resistance with a multimeter.

If you want to overdo it, you can substract cable resistance from the resistor value, so yor 56 ohms would end up at say 47 ohms. But you don't have to, if the LED is aimed at the receiver, even from the other end of the room, it will probably work even with much less current than 30mA.

Schematic:



Use any NPN BJT that will take the current, like BC337 or 2N2904. 1k base resistor gives 2.7mA base current, that'll be plenty to saturate the transistor. R5 value should be 47-56 ohms, and VCC should be 3.3V from your Pi. You can use 5V too if you have a 5V supply in your device already, this should be the case if the Pi is powered from a USB "charger". In that case increase the value of R5 to (5-Vled-Vcesat)/30mA = about 100-120 ohms.

Note the resistor is best placed on the transistor side, not at the other end of the cable with the LED. This will protect the transistor if the two wires get shorted.