You could actually get a payload into LEO with an ICBM, as long as it was lighter than your average nuclear warhead (or for MIRVed missiles, lighter than your warheads plus bus).
Also, isn't US fond of using old ICBMs to launch military satellites?
https://en.wikipedia.org/wiki/Lunar_Atmosphere_and_Dust_Envi...
EDIT: But you can download the realistic solar system mod to get a sense of what real world thrust ratios and orbital delta-v is like. And Children of a Dead Earth has multi-body physics for Lagrange points and so on.