Heat the oil in a cast-iron skillet over medium heat.
Add the onions and bay leaf and stir well to coat.
Season lamb burgers with salt and pepper.
Cover and cook undisturbed for 10 to 15 minutes, until soft.
Add lime juice and stir well.
Adjust the seasoning and raise the heat to medium-high.
Cook the onions uncovered for another 10 minutes or more, stirring from time to time to avoid scorching, until the onions are golden brown.
Remove the bay leaf and adjust the seasoning.