Tip: Look for shiny strawberries with a deep, even red hue (no white shoulders). Keep refrigerated for up to 5 days.
Reserve 1 cup strawberries and 1/2 cup raspberries for topping; cover and refrigerate. In a medium saucepan, place remaining strawberries and raspberries with 1 Tbsp. water. Simmer over medium-low heat, stirring occasionally, until berries break down, about 7 minutes. Strain mixture through a sieve set over a bowl, pressing on solids. Discard solids. Stir in honey and lemon juice. Let cool.
Preheat broiler and position rack 6 inches from heat. Lightly grease and flour a baking sheet or coat with baking spray. Cut cake into 16 1/2-inch-thick wedges, then cut each wedge on the diagonal to form 2 triangles. (You should have a total of 32 triangles.) Arrange cake triangles on prepared baking sheet and broil, turning once, until golden brown on both sides, 30 seconds to 1 minute per side. (Watch carefully to avoid burning.)
Immediately transfer warm cake triangles to serving plates. Spoon sauce onto plates and top with reserved strawberries and raspberries.