I emailed NJ Fish and Wildlife to get clarification on this and here is the explanation I got:
"New Jersey has a recreational lobster license. It allows the individual to have 10 traps with a limit of 6 lobster per day (within the legal size limits); the individual is not allowed to sell them. The Bureau of Marine Fisheries supplies tags for the lobster pots when the license purchase is completed. Federal regulations require ALL lobster pots to be tagged, serious fines are issued if this is not followed. For a NJ resident, the license fee is $102.00. For non-residents, the license is 10 times that, or $1002.00. For the resident license our regulations require that a person be a legal resident - having a second home in New Jersey does not meet that requirement. Proof of residence, ideally a copy of a NJ driver's license, is required when purchasing your license.The license is only valid in State waters, which is from the shore to three miles out. You can scuba dive for lobster and this does not require a license or proof of residency. BUT, you have to catch the lobster by hand, no spearing allowed. Again, you must stay within the size and quota limits for recreational lobstering."
Obviously, if you do not have a NJ drivers license, paying $1002 for the license isn't realistic.