Toast almonds in preheated oven, stirring every 2 minutes, until lightly browned, 5 to 10 minutes; transfer to a large bowl. Add chicken and mango chutney to the bowl; stir.
Melt butter with olive oil in a large stock pot or Dutch oven over medium-high heat. Cook and stir onion, celery, and garlic in melted butter until onions begin to soften, about 5 minutes. Add tomatoes with juice and raisins; continue to cook, stirring frequently, until the raisins plump, about 10 minutes. Season the mixture with curry powder and cayenne pepper; stir.
Pour chicken stock into the pot; add the chicken mixture, wild rice, apples, parsley, and lemon juice. Bring the mixture to a boil, reduce heat to medium-low, and simmer until the apples are tender yet retain some crispiness, about 5 minutes. Season soup with salt and pepper.