It states the service ceiling of the CF-104 being 58,000 feet, and normal operation at 48,500 feet also. I will admit that it's zoom-climb ability is impressive, but that's factory fresh. And the CF-104 that achieved Canada's altitude record was modified.
If I wanted I could state the Lightning can beat the F-15 in a sustained climb to 30,000 feet because a stripped down T.5 Lightning did so. The F.3 Lightning that zoom-climbed to 88,000 feet was fully laden.
I do not believe the F-104 could achieve greater heights, or speeds than the Lightning without modification which would make it incapable of combat.
The F-104 never had a thrust:weight ratio that equalled 1:1 , the Lightning would do at some point in it's climb. The Lightning was actually faster than the F-104 anyway, at Mach 2.3 recorded. Since the real records for the Lightning have yet to be released , the zoom-climb to 88,000 feet is just a story. The official records are yet to be released , and I'm eagerly awaiting them.
Anyone with a bit of sense would realise the Lightning can out-climb and out-pace the F-104. You rely too much on world records without realising that world records open the abilities to the public - think if the SR-71 true records were released !