Regulating the industry in a country like the DR is next to impossible. The lobsters will get smaller and smaller until the fishery crashes, and then it takes 6-10 years to recover. I expect it's happened sometime in the past 30 years once tourism got off the ground.
The resource gets more scarce, the market price goes up and they will spend more time and money fishing for them. Classic Tragedy of the Commons syndrome. I wouldn't be surprised if they aren't already importing frozen tails into the DR. Saw some tails at a COSTCO the other day for over $15 a pound. No wonder they're getting over-fished. I bet the fishermen are lucky to get a quarter per tail.
The good news is the fisheries do recover because of the lobsters' planktonic stage. They float around the Caribbean currents for a while so the DR will get new lobsters from upstream every year.
I understand many of the fishermen in the DR still use traps. Many of them get lost, and then they continue to catch lobsters for years, even decades. Since lobsters seek shelter, they'll go into empty traps and because they're cannibals, once you get one lobster in the trap, it will continue to self-bait itself. In the industry, these are called "Ghost Traps." Modern traps are designed with panels that rot away in a couple years to prevent this.
Cuba and Bermuda use a system of artificial shelters instead of traps. Then when they go to catch them, many escape, which keeps the fisheries sustainable. Very simple in design, but easier to fish than reefs. It protects the lobsters from their natural predators and may even increase the population.