This applies to "A person fishing in ASMFC Lobster Management Area (LMA) 4 and/or 5...shall not take or attempt to take, land, have in his or her possession, sell, or offer to sell any American lobster during the closed season of April 30 [February 1] through May 31 [March 31] inclusive."
http://www.nj.gov/dep/rules/adminchg/20150105a.pdf "A person fishing" applies to all gear types including recreational "fishing". "ASMFC Lobster Management Area (LMA) 4 and/or 5" includes our entire coast.