With a lobstering license in Maine, there is no maximum catch of lobsters you must abide by, like in other fisheries. Limits are set on number of traps, and timing of when traps may be set, but are not determined by actual number of caught lobster. However, sometimes you cannot keep all the lobsters you catch. In Maine both size and gender affect whether a lobster is a “Keeper” or not.
Sex Regulations
Female berried lobsters are off-limits to lobstermen, and even females who were at one time berried could be off-limits even without eggs. When a female lobster who is berried is hauled in a trap, lobstermen are required to “v-notch” the tail flipper to the right of center to indicate she was once caught as an egger. Females will eventually release their eggs in batches, but the v-notch will remain through several molting cycles. This allows the females to continue reproducing and populating the Gulf of Maine with another generation of lobsters.

Maine has a zero-tolerance law for any female lobster caught with any deformity to the flipper right of center for this reason. As it turns out, 15-20% of lobsters caught in Maine are released because they are v-notched females, and even more from not meeting sizing requirements.
Our earlier section 1.3 Reproduction and Life Cycle gives more information on how many eggs females produce, how they mate, when eggs hatch and more!
Size Requirements
On average, a trap that is hauled containing at least 2 market sized lobsters is a good catch. Minimum and maximum size requirements exist for lobsters caught in Maine; the minimum size requirement being a length of 3 ¼ inches and the maximum being a length of 5 inches. The minimum and maximum size requirements are based on the length of the lobster’s carapace or body shell. To keep a lobster, it must fall between these two lengths, anything below 3 ¼ inches or above 5 inches in length constitutes an illegal lobster and therefore an illegal take. Lobstermen are equipped with a gauge to assure lobsters are within the size requirements.

There is more information on size regulations under 4.2 Size Regulations. This page gives you a good look at how these regulations were set and how this makes the lobster industry more sustainable!
More info on laws: https://lobsteranywhere.com/seafood-savvy/maine-lobster-laws/