Years ago space settlement advocates were working out ambitious schemes for orbiting colonies housing 10,000 people. They were to be built of lunar-derived materials and would have been occupied primarily with building dozens of huge power satellites. Given the known resources on the Moon, and its advantageous location for interplanetary flights, has there ever been a design for a LUNAR-BUILT spacecraft to go to Mars?
There have been lots of plans for Lunar built spacecraft. There have been few that have been credible, and all are in the realm of speculation.
At present, any such plans are relegated to either distant conceptual plans (NASA, ESA, and ФКА/Roscosmos), fuel processing only (NASA and ESA), or science fiction literature.
Distant Conceptual Plans
NASA, ESA, and Roscosmos all have had conceptual plans for lunar construction and lunar bases since inception. None of these are even to the practical testing stage. NASA is funding some specific technological testing by college students in a variety of fields; I don't know about ESA nor Roscosmos testing towards it.
NASA has recently had some funding that lead to testing of the ability to seal up natural lava tubes into pressure habitat structures. Likewise, they've made chemically comparable ground regolith and tested it for cement and concrete usages. These are extremely early steps towards the "eventual" lunar construction base.
The actual plans themselves are little better than science-based whimsy - without major changes to the funding, none of them are likely to see any major progress.
Fuel Only plans
A number of NASA plans involve automated harvesting of lunar water to make O2 and H2, then shipping that fuel to an orbit assembled spacecraft for orbital fueling. By launching with tanks dry, the mass of the booster stage can be much reduced, allowing for a larger tank size per unit, and fewer earth to LEO missions to assemble the final martian mission; similar units would refuel the lander at mars, and possibly also the transfer vehicle.
Of the various plans, these, which don't actually meet the question's narrowest scope, are the only ones likely to be used. The technology exists, the water exists, the robotics can be made to perform the needed tasks. The Mars missions on the drawing board are looking at various methods of getting fuel into orbit, and lunar water is one that is getting serious consideration.
Pretty much all other variations are speculative fiction. Many science fiction stories include plausible human habitation on Luna, and manufacturing located at the lunar habitats. A few of these rise to credible plans. Most make assumptions about some form of fusion power and high efficiency electric thrusters, both of which are plausible but not yet implemented technologies.
The best rise to or exceed the quality of what NASA has released, but unlike NASA, there is little chance of these being implemented.
The advantage of building on the moon is that it is a shallower gravity well than earth, so requires less propulsion to get to Mars (or elsewhere). The major disadvantage is that (for the foreseeable future) it is very hard to operate there-there is not infrastructure. Remote operations are extremely difficult under these conditions. If we get to the point of an infrastructure on the moon appropriate to build a spacecraft, technology will have advanced so much that any design done now would be useless.