Because Lockheed had more 'influence' than any other contender?
Let's look at what was available in 1958-59 when the selections were taking place. The requirement was for an airplane capable of low-level delivery of a nuclear weapon, or a reconnaissance pass) at high speed and as much range as possible, with an all-weather navigation system; and capable of acting as a missile-armed interceptor with an AI radar, missile armament, and capable of Mach 2 at 50,000'+.
The contenders are the English Electric Lightning, Saunders-Roe SR.177 Jet-Rocket Fighter), Dassault Mirage III, Grummand F11F-1F Super Tiger, and the F-104.
The Lightning at that time was the F.1 version - fantastic acceleration and rate of climb, Limited to Mach 1.7 due to stability, 2 Firestreaks, and enough range to defend the end of the runway. No air-to-ground capability.
The SR.177 was non only a Paper Airplane, the British Government had officially stated that they weren't developing any manned fighters any more. You want it, you pick up the project from scratch.
The Mirage III was flying as a prototype. No air-ground weapons or nav systems. Armament 2 30mm guns and a single Matra R.530 missile. If you wanted the fast climb/acceleration rocket pack, you left the guns at home, and carried a single missile with a lower Pk than a well-thrown rock. Marcel Dassault didn't want to do any of that air-to-mud stuff - until he saw people buying it later.
The Super Tiger was flying, showed some potential, but had no radar, nav, or weapons clearance of any kind. It had also demonstrated very dangerous flutter characteristics, requiring a structural redesign. Grumman wasn't really pushing the airplane, using the contest as a way to build up its foreign sales department.
The F-104 - Already flying, already hitting all the performance points, in squadron service, cleared for all air-to-air and air-to-ground weapons. If you're interested, you hop on a plane to the States, and they'll put you in the back seat of a B or D model and take you up to Mach 2/50,000', and they'll let you talk to the Squadron Maintenance Officer about what it takes to run the jet and keep it flying. Then they'll put you into their Pinnochio-nosed DC-3 and let you play with the radar and nav systems.
Everybody else had, at best promises. Lockheed had an airplane.
Was there money trading hands? Yep. Was it against the law? At that time, no. In German and France, at least, at that time, it was not unlawful for people with some manner of connections to be paid to facilitate a sale. It was how business was done. That changed in the early '60s. (Personally, I suspect that was due to Dassault getting outbid) - Manufacturers paying connected people to facilitate sales was made illegal in the U.S. in the early 1960s, and in Europe in the late 1960s, early 1970s. Doesn't mean that the practice stopped, just became more complicated.
I recall an Op-Ed in Strategia y Defezia (European military magazine) in the early 1980s from a non-American/non-European (Posted anonymously, to avoid, uhm, indiscretion) Admiral writing about the difficulty of selecting equipment for his Navy. American stuff would have been great, but it cost a ton, the Americans wouldn't pay bribes, and they'd shut off support if your government did something they didn't like. The French and Italians were good at bribes, but not so swift on delivery and support. The Soviets stuff was last choice, and the had nothing to bribe with.