LR-60 Captain reported a Controlled Flight Toward Terrain (CFTT) event while executing a RNAV approach that had been assigned late after they had briefed another approach. Their FMS did not reflect an intermediate fix or corresponding altitude which led to an ATC Low Altitude alert and Go around instruction.

Narrative

On Day 0 Aircraft X; a Learjet 60; descended below the MEA and intermediate fix crossing altitude on the RNAV (GPS) at ZZZ. Subsequently a go-around was issued by ATC; the approach was flown again to a successful landing Runway XX.We were originally issued a hold on the way to ZZZ; all airplanes requesting the RNAV (GPS) approach were issued holds. Another aircraft questioned how an airplane just landed and was told that the only airplanes getting in are flying the localizer approach. We then requested the localizer approach and we setup/briefed the approach as published. As we were being vectored to join the localizer we were then issued the RNAV (GPS) instead; a few miles from ZZZ VOR. After adjusting the FMS to now fly the GPS approach we crossed ZZZ at 13;000 ft. and started the approach.The fixes in the FMS were as follows: ZZZ [VOR] -> ZZZZZ -> ZZZZZ1. Missing from this approach; in the FMS; is the intermediate fix 'ZZZZZ2' that has a crossing altitude of 12;900 ft. Not seeing this fix in the FMS; and having previously briefed a different approach with little time to set up and brief a completely different approach; we proceed down to the final approach fix altitude of 12;200 ft. at ZZZZZ. Upon leveling off we were given a 'low altitude alert' from ATC stating the MEA in that sector is 13;000 ft. This was the first indication in the cockpit that something wasn't right; we immediately started a climb. We were then told that ZZZZZ2 has a crossing restriction of 12;900 ft. After slight confusion in the cockpit for a second of 'what fix?' a go around was initiated. Not even two seconds after that a go-around was issued by ATC. The go-around was flown as published and the approach was then again initiated and flown to a successful landing.Further exacerbating the situation was the FMS not recognizing the approach as an approach but simply waypoints; because of this the VNAV was not usable for the approach. To avoid a similar situation care should be given when accepting a new approach so close to the initial approach fix when a different approach had been setup and briefed. Further verification of any intermediate fixes and crossing altitudes; not just the initial and final; would have helped had time permitted.