The output current will depend on the voltage difference on the LM317.
A heasink will be a must for higher currents.
Also when the decoupling capacitors are missing the LM317 will heatup, due to possible oscillations and shutdown.
Another trick that provides relief similar to that of lowering the input voltage is to shunt some of the current around the LM317 using resistors. The current through your resistors (between input and output) can be no higher than the minimum load. If your power supply is going to be variable the matter becomes much more complicated.