Combine butter, honey and lavender in a small saucepan and heat, whisking occasionally, until butter is melted and mixture is just coming to a simmer. Remove from heat and let sit in pan for 30 minutes. Remove lavender and discard. Pour syrup through a fine strainer and into a bowl or measuring cup to remove any stray lavender leaves.
Preheat gas grill to medium and lightly oil grate. Place all fruits on a rimmed baking sheet and brush with honey glaze. Grill until fruit is heated through, slightly tender and caramelized - about four minutes total for bananas, six for pineapple and peaches. As the fruits cook, brush them once or twice with additional glaze and turn once. Serve immediately with a scoop of vanilla ice cream if desired.