In a small saucepan, melt the butter over medium heat; cook mushrooms and onion, stirring occasionally, for about 5 minutes or until onion is softened.
Add garlic, cream, lemon juice and salt; cook, stirring occasionally, for about 5 minutes or until the sauce reduces to half and thickens enough to coat the back of a spoon.
In a shallow dish, mix together flour, dill, salt and pepper. Gently press the fillets into the flour mixture, turning to coat, and shaking off the excess.
In a large skillet, melt the butter over medium heat; cook fillets for 2-3 minutes. Turn and sprinkle with lemon juice; cook for about 3 minutes or until the fish flakes easily when tested with a fork.