Similar questions came up back in the last days of Mir. There are several problems with it.

1. The ISS is orbiting the Earth at about 17,500 MPH. To achieve that figure-8 between the Earth and the moon, you'd need to accelerate it to approximately 25,000 MPH.

2. The ISS is massive. Even in the "weightlessness" of orbit, it takes energy to accelerate mass. Your ion engines would have to be the most powerful ever built (the biggest one that I've ever heard about generated maybe 1 pound of thrust) and would take a lot of electricity to operate. Some of that thrust would be needed to overcome the minute amount of drag at the ISS's orbit, so the net thrust for acceleration would be less than the total provided by the ion thruster.

3. Once you raised the orbit very much, it'd be too high to be reached by Progress resupply ships or the Soyuz and Shuttle manned spacecraft. That means you'd need something more powerful to send supplies and crew to the ISS. In addition, once you've achieved the figure-8 orbit, the ISS at perigee would be doing about 25,000 MPH as it swung by the Earth. Once again, you'd have a more difficult time reaching and docking with the ISS.

4. The ISS wasn't built with the shielding to protect for the higher radiation levels of the van Allen belts. While it's true that it would only take 30 minutes or so to pass through the belts each time, the higher radiation levels at and beyond the belts could cause problems with the ISS's electronics. High energy radiation can cause "single event upsets" in things like memory chips and microprocessors. While it's almost certain that the ISS uses hardened components, they might not be sufficiently hardened for higher radiation levels.

5. It only takes 3-4 days to travel between the Earth and the moon. While it'd be more comfortable to travel in a roomier vehicle, it just doesn't seem worthwhile for such a "short" trip.

6. Once you reached the moon, the ISS would be traveling approximately 6,000 MPH. The crew would have to either quickly decelerate to a landing or at least to orbital velocity (about 4,000 MPH).

7. When it came time to leave the moon, you'd have a similar problem to that experienced by crews taking off from the Earth - you'd have to quickly accelerate to catch the ISS as it swung by because it couldn't slow down to meet you.