For the glaze: In a small saucepan, bring the honey, lemon juice, and lemon zest to a boil over medium heat. Boil for 1 minute until smooth. Set aside to cool.
For the cream: In a medium bowl, using a hand mixer on medium speed, beat the cream until thick. Add the sugar and beat until the cream holds stiff peaks. Beat in the yogurt, rum, and vanilla.
For the fruit: Place a grill pan over medium heat or preheat a gas or charcoal grill. Sprinkle each side of the pineapple slices with brown sugar. Sprinkle the cut sides of the bananas and grapes with brown sugar. Grill the pineapple until grill-marked and golden, 4 to 5 minutes each side. Grill the bananas and grapes until lightly browned and warmed through, 2 to 3 minutes each side.
Place the grilled pineapple on 4 plates. Top with 3 banana slices and 3 grapes. Drizzle with honey glaze and spoon a dollop of the cream on top. Garnish with chopped fresh mint and serve.