Seasonal Seafood Restaurant Nantucketlobstertrap.com. Nantucket Lobster Trap Restaurant & Companies. The Nantucket Lobster Trap restaurant is a family owned business that has been in operation since the early 1980’s. We have recently expanded to include Food Trucks which service the local Cisco Brewery and private functions. Last year we debuted our newest ‘Take Out Window’ program. Food service operations take place April through December. The N...