Remove the lobster meat from the shell and cut into small chunks. Heat a skillet or cast-iron pan until very hot, then add enough oil to coat the pan. Add 1 tortilla to the pan. Sprinkle the goat cheese on half of the tortilla then distribute ¼ of the lobster meat, a few slices of avocado and jalapeño, if using, on the same half. After about 2-3 minutes, carefully close the quesadilla by placing the empty half on top of the other ingredients. Press down to make sure it sticks together and cook for about another minute, flipping if desired, until cheese is melted.
Serve immediately with a squeeze of lime juice if desired, and, you can of course serve this with more avocado, guacamole, or even a fresh salsa.