No, the only Dragon type move Lucario can learn is Dragon Pulse.
Sadly No... I wish it could! The only Fire type move Lucario can learn is Sunny day.
Lucario learns Dragon Pulse at level 47.
Lucario learns Aura Sphere at level 37.
at level 51 it will learn extremespeed
aura sphere
27 my lucario learnt aura sphere lv37
47
32
level 37
Yes, at level 42 Lucario learns Close Combat.
Lucario learns Aura Sphere at level 51.