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Around 270 million lobsters are killed each year.
The actual number of Lobsters killed is difficult to get exact. The number is measured in weight rather than number of lobsters. Additionally not all regions publish their numbers. The United States reported 93 million pounds of American Lobster in 2019, Canada reported 100 million in the same year, Australia and New Zealand reported 22 million combined. From here we can extrapolate values for other regions based on estimated consumption. Lobsters vary in weight, ranging between 1 and 5.5 pounds. If we combine global numbers and divide by the weight, we get to roughly 270 million. This is an estimation and actual numbers might vary.
As with other fish, Lobsters are often caught in the open ocean. Fishing often results in bycatch, where animals other than lobsters are caught unintentionally. This can cause significant harm to local ecosystems as it decreases the population of all fish. Additionally, high demand leads to overfishing, which drastically reduces populations. This doesn't harm just the lobsters, as species are often very interconnected. Many other animals will die as a result of lobsters being wiped out.
It has been proven that lobsters, amongst many other ocean animals (cephalopods and decapods), can feel pain. They are sensitive creatures. They can learn to anticipate and avoid pain, just like many other animals. Unlike other animals, lobsters can't go into shock. When humans are in so much pain they can't handle it, we go into shock, essentially blocking out the pain when it's too great. Lobsters suffer much longer when in pain. This is especially cruel when you realise that traditionally they are boiled alive. They suffer greatly in their final moments.
Unfortunately death isn't the only moment they suffer. Lobsters feel great emotional stress as they are taken out of their safe space. When placed in new environments, especially crowded ones, they get very anxious, which might even lead to depression.
Various sources were used for each animal. When numbers differed the average was taken, depending on which most sources seemed to agree on. When ranges were given the lower end of the range was used.
Lobsters: https://www.reportlinker.com/clp/global/4436, https://www.britannica.com/animal/lobster, https://animalsaustralia.org/our-work/compassionate-living/6-incredible-lobster-facts/, https://animalsaustralia.org/our-work/marine-animals/crustaceans-lobsters-octopus-sentient-feel-pain-laws-uk/, https://www.columbia.edu/~col8/lobsterarticle.pdf