Why A standard pi network is shunt capacitor, series inductor, shunt capacitor. A Pi-L adds one more series inductor after the output shunt capacitor, so the circuit becomes a pi section feeding an L section. That extra element gives a steeper rolloff above cutoff and better harmonic attenuation, which is why Pi-L tank circuits are favored in tube power amplifiers, and it also lets the transformation be done in two smaller steps for a higher loaded Q at the tube end.
Watch out The three-discrete-parts description fits the plain pi network itself; the Pi-L has four reactive elements, and both shunt capacitors are referenced to ground, so nothing is floating.
Pi plus L: pi network first, then an L section. Four parts, extra series coil at the output for extra harmonic rejection.