Stir together olive oil and lime juice. Brush avocados all over with olive oil mixture. Sprinkle cut sides of avocados with salt.
For charcoal grill, grill avocado halves, cut side down, on the rack of an uncovered grill directly over medium coals for 5 minutes or until browned. Turn avocado halves, cut side up. Fill centers of avocado halves with the 1/4 cup picante sauce and shredded cheese. Cover grill and grill about 5 minutes more or until cheese begins to melt. (For a gas grill, preheat grill. Reduce heat to medium. Place avocado halves on grill rack over heat. Cover and grill as above).
Remove avocados from grill. Sprinkle tops of avocado halves with snipped cilantro. If desired, serve on a bed of salad greens with additional picate sauce and sour cream.