In a small bowl, mix together tequila, melted butter, oil, lime juice and garlic. Let stand for at least 15 minutes.
Preheat barbecue for medium heat.
Brush cooking grate with vegetable oil. Brush mushroom slices with tequila mixture and place on barbecue. Cook until the mushroom slices begin to wilt then turn and brush with more of the tequila mixture. Cook for a few minutes until mushroom slices are tender. Watch carefully so they do not burn.