phase II is out for the forseeable future, look for it in 2030 perhaps - it would require a whole new fundraising drive, which the museum isn't going to start anytime soon.
and many of the donors for Phase I haven't pulled through yet, it's getting interesting.
The lawn hasn't been a lawn since at least the Pei addition. The new parking lot replaced an old parking lot. At least the new lighting fixtures and markings are far more attractive in the meantime, as we wait another 15-30 years to get phase III.