In early 1953, Lockheed proposed its Model L-242 in response to the Navy's requests for proposals meeting its Outline Specification 130.
One reason that this was plausible was that the original XF-104 had a shorter fuselage that the production F-104 overlay shown here in gray, which reduced empty weight.
Although the proposed design had zero dihedral, subsequent wind tunnel testing would have resulted in five degrees of anhedral.
It was of course, very unlikely that the Navy would have trusted Lockheed, which had essentially zero carrier-based fighter experience (there was a modified P-80 that was evaluated at-sea*) with a contract for one even if none of its favored suppliers bid. As it happened, Vought won the competition with what was to be the F8U Crusader. And that bet was hedged by contracts to North American for the FJ-4 Fury, Grumman for the F11F Tiger, and Douglas for the F4D-2 (F5D) Skylancer. Only McDonnell was left out, which was worrisome for a time in St. Louis, but the consolation prize led to the F4H Phantom.
One footnote to the Navy Zipper (the sound and impression it made on a low, fast flyby) story was a modeler's April Fools article about the Navy modifying two F-104s for carrier operation, for which photos of two F-104s being used to test the Sidewinder at China Lake (or maybe just to get some flight time in one) added plausibility.
* See http://thanlont.blogspot.com/2012/02/navy-shooting-stars.html