Place the bread in the bowl of a food processor and process to form coarse crumbs. Add the lentils, parsley, garlic, cumin, coriander, tomato sauce and egg. Season with salt and process until smooth. Transfer to a bowl and set aside.
Place the flour on a plate. Divide the lentil mixture into 4 even portions. Use lightly floured hands to shape each portion into a round 8cm patty, about 2cm thick. Lightly coat each patty in flour.
Heat oil in a large non-stick frying pan over medium-high heat. Cook the patties for 2 minutes each side or until golden. Drain on paper towel.
Whisk the vinegar, mayonnaise and lemon juice in a small bowl until well combined. Taste and season with salt.
Top the bread roll bases with avocado pulp, beetroot, a lentil patty, rocket and lemon mayonnaise. Serve immediately with bread roll tops.