In a small bowl, whisk the vinegar with the lemon juice, celery seeds, mustard and half of the garlic. Gradually whisk in 1/4 cup of the olive oil and the almond oil until emulsified. Season the dressing with salt and pepper.
In a mini food processor, combine the remaining garlic with the parsley, celery leaves and almonds and pulse until finely chopped. Add another 1/4 cup of the olive oil and puree to a chunky paste. Season the pesto with salt and pepper.
Light a grill. Brush the mushrooms with oil and season with salt and pepper. Grill over high heat, turning once, until tender and browned, about 5 minutes. In a bowl, toss the grapes with the remaining 1 tablespoon of olive oil and season with salt and pepper. Grill over high heat until the skins begin to blacken in spots, about 3 minutes; line the grill with perforated foil if the grapes will fall through. Transfer the grapes and mushrooms to a large bowl and toss with the pesto.
Arrange the lettuce leaves on a platter and drizzle with half of the dressing. Spoon the mushroom-and-grape salad onto the lettuce. Toss the celery with the remaining dressing, spoon it on top and serve.