The Lamb-Baker house at 88 Newtown Lane, which East Hampton Village purchased in 2007 for $1.4 million — and which Robert Hefner, an historic preservation consultant, called “a pretty ambitious Greek Revival-style cottage” — has been sitting unused for several years, but now, the property, perched next to the East Hampton Middle School, is ready to be renovated, Mr. Hefner said at the village board meeting last Thursday.