No Laura, that was the building that houses the motor & cable for the cage that travels over the water to get to the LH.

"The usual way of getting to and from the Nubble was by boat. For a time, the keepers used a bucket suspended on a line across the channel to transport supplies. This system, installed in the 1950s, was never intended for the transport of people." from: http://www.lighthouse.cc/capeneddick/history.html

Note: this is one of the few Lighthouse photos where the wires were not a distraction.