The front lunge mimics the specific muscle group engagement that you get when running or hiking down hill. There for it can be used (doing just several reps) to strengthen the muscles supporting the knee so that running or hiking down hill (where you are going to be doing many thousands of repetitions). Obviously if you experience severe knee pain when doing lunges you need to investigate the cause and remedy it. For mountain runners this typically tight vastus lateralus (lateral quads) pulling the knee cap to the outside. Get after those quads with rolling exercises. I’d say 90% of our atletes that have this issue get relief this way.
AS for the box step down. We’re trying to mimic the strength demands and mechanics of stepping down a big step in the mountains. Many rough trails will require this movement. Steping to the side if the box is a good exercise but does not mimic the down hill runner/hiker’s movements very well.