Soak onions in milk and water for 30 minutes to remove some of the harshness. Drain and spread on towels.
Preheat oil to 350 to 370 degrees. Dip onions in batter and fry, for about 5 minutes until light brown; drain on absorbent paper.
To fry mushrooms, cut stems 1/4-inch below caps. Wipe caps clean with paper and sprinkle with lemon juice and salt. Heat vegetable oil to 375 degrees. Dip mushrooms in fritter batter and fry, 2 to 3 minutes or until golden brown.