FAQ:

How to tell the difference between a male or a female?

How do lobsters mate?

How many eggs do females produce?

How many of the lobster larvae will survive?

You may be able to identify the sex simply by looking at its tail: Females tails are wider because that is where she carries her eggs. The other way to determine a lobster’s sex is to look at its first pair of swimming legs: When you turn the lobster over and look under the base of the tail, you will see a pair of legs that look different from the rest: If the pleopods are feathery and soft, it’s a female. If they are harder and stiffer it is a male!

Lobsters can only mate after the female molts. Before that stage, the female releases pheromones (chemicals) into the water to let nearby males know she is preparing to molt and mate. Males will fight for the female and the lobster that wins the fight will take the female into his cave and protect her from predators. Once she has shed her hard exoskeleton, the male gently turns her over and pierces her abdomen with his first pair of pleopods. He deposits sperm packets into her sperm receptacles; these she will store for up to 15 months before she releases eggs.

http://www.maine.gov/dmr/science-research/species/lobster/guide/index.html

When the female judges the time is right, she releases the eggs which pass by the seminal receptacle and are fertilized with the stored sperm. The female then attaches the eggs, all 5,000 plus of them [some older females will carry 100,000], under her tail with a glue-like substance where they will stay for the next ten to eleven months. During this time, she is called a berried lobster because the eggs look like small berries.

NH Fish and Game youtube channel

When the eggs hatch, the baby lobsters don’t look like their parents. These small larvae will molt four times before they start to show any resemblance to an adult lobster, then another 20 times over six to eight years before reaching the legal size for harvesting in Maine. When they are small larvae, the baby lobsters float at the surface of the ocean. Not many of the millions of eggs hatched each summer will survive this first stage of their life; small lobsters are snack food for dozens of other marine species. Once the small lobsters have grown out of the first larval stages, they move to the ocean floor to find protection in seaweed and rocks. There the juvenile lobsters will stay hidden until they are large enough to fight off predators.

Baby Lobsters Look Like They're From Another Planet | Popular Science
American lobster larvae! https://www.popsci.com/baby-lobsters-look-like-aliens/

Learn about how they molt—>