That isn't how the Apollo missions worked. They put the command module, service module and the LEM on a single Saturn 5[1]. Once in space, the command+service module would need to turn around and dock with the LEM before heading off to the moon.

https://www.nasa.gov/history/diagrams/apollo.html

1: https://www.nasa.gov/wp-content/uploads/static/history/diagr...

> Apollo missions used two launches of the Saturn V - one for the crew capsule and one for the lunar lander, which rendezvoused in orbit.

That was a concept called "Earth Orbit Rendezvous" which was discarded early on during the Apollo program in favor of "Lunar Orbit Rendezvous" where the Command and Service Module (CSM) and the Lunar Module (LM) was launched on a single Saturn V. You can see this in the movie Apollo 13.

> Apollo missions used two launches of the Saturn V - one for the crew capsule and one for the lunar lander,

What? Have you watched any Apollo mission media ever?

Watch Apollo 13 the movie at least and get the most basics of facts straight.

Starship must utilize refueling. It can't get to, land on, and return from the moon without it.

That's a matter of some debate. Somewhere between 6 and 12, I believe, is the range.

SpaceX plans to stretch the second stage to increase fuel carrying capacity for tanker flights, so the actual number is TBD until both the revised Starship and its engines (Raptor 3) are built and tested.

It depends on how many Starships you can launch simultaneously, because the time the fuel depot spends in orbit determines how much fuel is lost to boil-off. If you have a serial launch architecture, assuming reusability, refuling and relaunching, then the upper bound is around 20 launches. Even with expendable Starships, this is still cheaper than SLS, but not by much... This is why reusability is critical to the mission.