Heat the olive oil in a medium skillet over medium-high heat. Add the carrots, onions, bell pepper and celery. Cook, stirring occasionally, until softened, 5 to 10 minutes. Set aside to cool slightly.
Meanwhile, whisk together the flour, baking powder, paprika and a pinch of salt and pepper in a large bowl. Whisk in the milk and egg until combined and smooth. Fold in the cooled vegetables, lobster meat and parsley.
Fit a baking sheet with a wire rack. Add enough vegetable oil to come about 3 inches up the side of a Dutch oven or heavy-bottomed pot. Heat over medium heat to 350 degrees F.
Using a 3-ounce cookie scoop, scoop the fritter batter and gently drop into the hot oil. Fry the fritters in batches until deeply golden brown, a few minutes per batch. Remove to the prepared baking sheet and sprinkle with salt while still hot. Repeat with the remaining batter. Serve warm with lemon wedges on the side.