Fishing around online for the lunges, looks like Step Ups (start by going up and down one stair, add weight or height as desired), squats (just go as low as your comfortable with and build depth with time) and single leg dead lifts are common recommendations.
Burpees looks like they might be a bit tougher to swap here as most of the alternatives have jumps still, but I am seeing Power Squats (squat, then up to a calf raise) and dumbbell thrusters (squat and rase a set up dumbbells to just above your shoulders, then stand and raise the dumbbells overhead) are viable alternatives.
So I guess work on squats and squat variations till you're ready.