Heat the vegetable oil in a heavy saucepan and brown the chicken meat on all sides. Remove the chicken and set aside.
Add a little more oil and fry the lentils for two minutes over medium heat. Add the mustard seeds and half the curry leaves and stir once. When the mustard seeds begin to pop, return the chicken to the pan and add the water. Season to taste and simmer 20-30 minutes, until the lentils are mushy. You may need to add more water.
A couple of minutes before serving, add the remaining curry leaves, simmer, then add the lime juice.