Does this Lear 35 have missiles on it?
No, it's not a missile, it's a towed target:



Towed targets are used for electronic warfare and gunnery training. The can serve as a radar target or visual target during military exercises.

The 'missile' is on a long cord and can be reeled from the aircraft. The pod that you see here is a MTR-101 reeling system with the capability to drag the target up to 30,000 ft behind the aircraft.

If you are interested in flying these kind of missions, it seems  L3 is looking for a new First Officer for their Learjets.