Although the Chase Beach area at Post Pond is for residents only, it is fine to park at the boat launch off NH-10 in Lyme and walk in.

One can also park at, or walk over to, the nearby Chaffee Nature Preserve, which has a wheelchair-accessible trail to a blind overlooking Little Post Pond.
From Jim Block

Pool Pond has a surface area of 141 acres and a maximum depth of 13 feet. The lake offers a view of Mount Monadnock and is part of the Pool Pond Protection Association, which aims to preserve the water quality and natural beauty of the lake. 

There is parking and canoe access to Pool Pond on Mountain Road.