The only purpose of the Saturn V was to lift all the componentry one needed for a lunar mission in one fell swoop. Something like 90% of the system’s fuel was relegated simply to achieving LEO. With the ISS, a huge proportion of the weight, and therefore cost and difficulty of contruction, is unnecessary.
A modern mission doesn’t have to carry re-entry heat shielding, for example, because the returning astronauts can just hop a shuttle down. The ISS also now has all the major componentry necessary to assemble itself, so construction of a lunar transit vehicle could actually be built as part of the ISS, then detached when the mission is ready.
By parking the old Columbia at the ISS, with a crew compartment (perhaps a refurbished Spacelab) placed in the bay, the ISS could house perhaps a dozen or more workers, and probably keep two or three on EVA at all times.
Furthermore, the combined launch facilities of NASA, ESA, Russia, China, and other potential players such as Japan, India, and the Department of Defense far outstrips the worldwide launch capabilities of the 1960s. Traffic control may actually be a larger problem than getting the necessary goods to LEO.
I’m betting that once a design is settled upon and the proper adaptors for the componentry are built, assembly could be completed in a matter of days or weeks.
Everything except the lander could conceivably be cobbled together from currently existing parts. With the ISS, chase-rockets could even be held on standby in case of emergency to deliver any replacement components. Aside from catastrophic failure or an uncontrolled burn, astronauts travelling to the moon would benefit from a much better system of redundancy and safety than they did under Apollo.
So I think the real question is, “how fast can you design and build a lunar lander and lunar space suits?” My guess is less than eighteen months, if you scrap all other missions in the pipeline and have complete support from all the worlds space powers.