The clothes do catch fire, the stump does not. You can see it happening:
The type of ignition that occurs is a self-ignition occurring on the material. Humans do not combust thanks to thermal inertia (the human body is 2/3 water).
Assuming the Jedi wear a basic cotton material, the self-ignition flashpoint (the material catching on fire) is 407 degrees C.
The lava flowing is viscous, flowing quite rapidly, and appears to go for kilometers, suggesting a rhyolite lava. This type of lava is unusually hot in the greater than 950 degrees C range.
Using the Sakimoto and Zuber: Flow and Convective Cooling in Lava Tubes Model and Anakin's slow descent down the loosely graveled walls we see that Anakin finally comes within range to trigger the self-ignition point of 470.