Combine all falafel ingredients except oil in the bowl of a food processor fitted with a steel blade. Pulse mixture until coarsely ground. Transfer to a bowl or container and refrigerate, covered, for several hours.
Form the falafel mixture into balls about the size of walnuts and press to flatten.
Heat 4 inches of oil to 375 degrees F in a deep pot or deep fryer. Fry about 6 balls at once for about 4 minutes, or until golden brown. Drain on paper towels. Stuff each pita with 4 falafel balls, chopped tomatoes, lettuce, and tahini.