Larry's tree falling is directly related to the confirmation of his death. The tree falls in the month of his birth, August. It falls when Ann, Larry's fiance, is sleeping in his room, having come for a visit to the Kellers' home.
Additionally, the fallen tree sits in the middle of the backyard, as a symbol of the presence of Larry in the middle of this play. Larry is present in the action in the presence of this tree. The characters, Joe, Kate, Chris and the neighbors have no choice but to talk about Larry.
So the tree acts as a catalyst for a deeper, more meaningful discussion of Larry and his fate. It precipitates Frank getting the horoscope for Larry in order to confirm if Larry is dead. So it is intrinsically related to the revelation that Joe Keller sent faulty parts to the military and is responsible for many deaths. The sad reality of Larry's suicide is linked to the falling of the tree.
The apple tree that was planted in a tribute for Larry is destroyed in a storm. This seems to signal rough times ahead, as well as the destruction of hope that Larry will ever be found alive.