The information I'm finding on the internet suggests Dragon 2 should run around 400 m/s of delta-V (it only needs on the order of 200 m/s to go from terminal velocity aerobraking to landed on Earth).
TLI to LLO is 800 m/s, and I'd guess that a Circumlunar return trajectory to LLO transfer would be on that order -- which is already out of the Dragon 2's range and you're only trying to get into orbit on the Moon, not return, and definitely not land or take off again.
Its close enough though that a beefed up Dragon 3 might be able to dock with some kind of space station and refueling dock in lunar orbit, then you just need to have a lunar ferry (Apollo sorta downsized all of this and crammed it all on top of a Saturn V for one-time use -- I'm thinking a bit bigger for the whole system and more cough reusable...)
However, the minimum delta V to land on the moon is ~1.72 km/s, and you need another 1.72 km/s to get back into orbit + some safety factor ~2.2-2.4 km/s. By comparison it takes ~8km/s to get from LEO to low moon orbit and back to earth. Though you can reduce this by how hard to hit the earth's atmosphere. So, having fuel to land and take off from the moon is not that much worse than getting to the moon and back.
No, from Earth LEO some 3.1 km/s will get you to TLO, and then some ~1 km/s will take you to Moon low orbit, so total about 4(+) km/s. 8 km/s is an approximate budget for a round-trip between low orbits.
Sending a couple of humans around moon for tourism is a waste of resources.
See: Apollo 8 mission.
Though I don't know why anyone would want to spend a week locked in a tiny can like that, let alone pay big bucks for it. There's a limit to the discomfort I'd be willing to endure for bragging rights.
People tend to think of the Moon as a "staging point" on the way to Mars, but in reality, it would be a significant detour.
The only craft SpaceX has that can land on Earth or the Moon is Dragon. I am pretty sure Dragon does not have enough delta-v to do a full propulsive landing on the moon (no aerobraking available) and then return to orbit. And they definitely don't have the tech to re-fuel in lunar orbit for the return to Earth. None of this equipment exists.
Not to mention that this would be a totally new lunar strategy, since the Apollo mission returned to earth in the lunar orbiter (Command Module) rather than re-fueling and returning in the lunar lander.