Cut away the brown skin and thin roots from the celeriac and chop the flesh into small chunks. Place in a saucepan of cold water with the lemon juice or vinegar added to stop the celeriac turning brown.
Add the potatoes and boil for 10 minutes or until the celeriac and potatoes are tender. Drain, place in a bowl and crush with a fork until roughly mashed.
Heat 2 tablespoons of oil in a large frying pan and fry the onion until softened. Stir in the carrots and thyme and cook for 2 further minutes. Add the crushed potatoes and celeriac and stir until mixed.
When cool, shape the mixture into 4 round flat cakes. Dust with the flour, dip in beaten egg and coat in the breadcrumbs. Chill the cakes in the fridge for about 1 hour so they firm up.
Shallow fry the burgers in hot oil for about 5 minutes until golden brown on both sides, turning once. Drain on kitchen paper and serve in toasted burger buns with lettuce, tomato slices and onion rings or as an accompaniment to chops, steaks or sausages.