They've boxed the trees and are repairing fences to the South, and will move around over to Cherry Hill and work on the shoreline. The small rustic pavilion is inaccessible, but the LP is still open.
UPDATE: The fence is up to the LP, and they've closed off the bridge and walkway by the Ramble, too. In talking to the work crews, they indicate that the work is on the southern shoreline first. But the permit office is still indicating that work will actually be done around the pavilion, so they have stopped issuing permits. We're going ahead with our booked weddings, but have alternative plans just in case.
If you have a permit for a wedding already, and your group is smallish, all may be well, or you may wish to call the permit office and try to rebook. We don't know how long this will last, so I'm not sure about Fall. Consider some of the other little rustic shelters around the lake for small weddings, or of course Cop Cot, the Belvedere (castle) terrace with the gazebos - here's a picture looking up from the Shakespeare garden, or even the Dene, on the East Side. Be creative - go NORTH to the lovely spots around the Mere and the pool - or try to book the terrace in front of King Jagiello which looks at the castle and the turtle pond. Explore the park!