Light a grill or preheat a grill pan. Brush the apricots with oil and season with salt and pepper. Grill over high heat, cut sides down, just until lightly charred, 5 minutes. Let cool.
In a bowl, whisk the lemon juice with the 1/4 cup of oil and season with salt and pepper. Gently toss in the apricots, radicchio and arugula. Transfer to a platter and top with the burrata, ham and vinegar. Serve.