Preheat oven to 120 degrees C. Line a baking tray with baking paper. Whisk eggs and flour in a bowl. Add whitebait, stirring until well combined. Season with salt and pepper.
Heat half the butter in a frying pan over medium heat. When hot add 2 tablespoon quantities of whitebait mixture to pan, making 3 fritters at a time. Cook for 2 minutes or until golden. Turn fritters and cook for a further 1-2 minutes or until golden and whitebait has turned opaque.
Transfer fritters to prepared baking tray and put in oven to keep warm. Cook remaining fritters. Serve with lemon wedges and avocado.