Let's strap a couple rockets to it and move it to lunar orbit. Empty it out of personnel, let it do a nice, slow burn to lunar orbit. Slower is cheaper in space. Let it take however long it does to get there, and then we can start sending unmanned Dragon capsules back out to resupply it and lunar shuttles via SpaceX. This would be a good "next step" toward eventually building a permanent structure on the lunar service, and could eventually serve as a sort of waystation for missions on the way out to Mars.
Bear in mind: The lunar soil is full of O3 and H3, which both make for excellent rocket fuel. An unmanned refinery on the moon could turn Luna into a gas station for any interplanetary mission at a fraction of the cost of lifting all that material out of Earth's orbit.
You forgot the small fact that the ISS is basically a collection of thin metal tubes with minimal thrusters. Some people have estimated that it would take about 150 years and about 150 fueling trips to make a lunar orbit transfer. I suspect the ISS couldn't take the stress of a burn that it would take to accomplish this in a reasonable amount of time (e.g., strap-on-rockets). Even if a tractable method was found, the ISS needs to be supplied by the Earth. Putting the ISS by the moon makes this exponentially more expensive (every kg has to leave our gravity well, not just make it to near-earth-orbit).
A more permanent lunar space station needs to be designed for the task (i.e., more self-sufficient), not a re-purposed piece of cold-war space history.