Place cilantro, parsley, pepitas, garlic, pepper flakes, salt, and black pepper into a food processor. Secure lid and begin processing. Slowly pour in olive oil through the top. Check for consistency and add another 1-2 tablespoons of olive oil if needed. The mixture should have a pureed texture. Taste for salt content and add a little more if needed. Set aside.
Preheat grill for medium heat.
Place lobster tails onto a cutting board. Using sharp kitchen shears, cut each one down the center lengthwise to create two halves. Briefly rinse under cold water to remove any debris and blot dry with paper towels. Spoon about 1 1/2 to 2 tablespoons of pesto onto the exposed flesh side of each halved tail.
Add lobster tails onto the grill, shell side down. Close the lid and let them cook for 8-10 minutes, or until the shells turn pink and the flesh has an internal temperature of 140 degrees F.
Once cooked, remove the lobster from the grill and place it onto a serving dish. Spritz with a bit of fresh citrus juice (lime if using cilantro, lemon if you are using just flat-leaf parsley). Enjoy!