Type in "astronautix.com" into your [search] window,
and surf your way over to the webpage listing types
of rockets.

I'll do better than that! The biggest Atlas-5 planned will
be able to park around 22-23 metric tons in LEO.

Coincidently, since the specific-impulse of LH2/LOX
is about 440 seconds, and the DeltaVee to send
a payload from LEO to the moon is around 3,200 meters/second.
The mass-ratio works out to about 2.2 [22,000kg (fully-fueled)/10,000 kg (Empty mass)].
Assuming that the 10,000 kg includes an "empty" Centaur upper-stage
(2000kg), then you can send 8 metric-tons of useful weight to the moon
by the Atlas-5.

The Heavy-Lift Delta-IV is even better [25.8 metric tons to LEO], and it doesn't apparently use strap-on solid boosters (according to astronautix.com).

What if Morton-Thiokol could work with NASA and Delta rocket engineers to fit two, strap-on shuttle-type SRB's onto a Delta-IV
to boost its payload from 25.8 metric-tons upto maybe 40-50 metric
tons to LEO? 40-50 metric tons to LEO could work out to 20 metric
tons sent to the moon (Close to the mass of the Apollo-8 moonship).

Jacob

"We will go to the moon, and do those OTHER THINGS, not because
they are easy, but because they are hard."
John F. Kennedy