For a major mission like this -- not that it has been funded -- it will likely take a bigger rocket than is currently in our stable. Of course, we used to have the Saturn V, but we let that go after all those successful trips to the moon, so successful that the program died from boredom. We even had extras on hand, which we basically destroyed. A precious few (one?) made it into museums. (Where do you put a 36 story tall rocket?)

Now, we have to hitch rides on Russian hardware, and even US hardware is using Russian engines.

It's shameful.

I think SpaceX will eventually develop high powered boosters. It would be nice to see them get booster recovery worked out first.
Virgin Galactic's approach might be just perfect for "low" orbit (eventually). Takeoff from conventional airport. Land at conventional airport. Satellite maintenance made easy.

Space Adventures got 2 paying customers, the third will be a pilot.

They'll go to ISS first, then dock with a separately launched booster for TLI.

The rockets and boosters already exist, what's missing is a lunar qualified capsule.

The Soyuz was originally designed for the race to the moon in the 60's, the production models have been optimized for ISS missions, so Russia is customizing a couple of them for lunar re-entry etc.