This particular lunge variation has recently become a favorite of mine. It takes two untraditional (for the most part) exercises – a front squat and backward lunge – and combines them into one fantastic movement. Shout out to @movementresilience and @barbellrehab for the inspiration. The backward lunge places the largest demand on your reference limb's (front leg) hip and knee extensors, simply due to the fact that you are bearing weight primarily through this limb throughout the entire movement. Additionally, because we are bearing weight through this limb throughout this exercise, there is a relatively high demand on ankle stability as well.
Now for the hand hold. With lunges, you can choose from a variety of holds that include dumbbells: dumbbells in either hand at your sides, a single dumbbell at the chest like a sumohold, a barbell racked on the back, or a barbell racked across the shoulders in the front. Choose whichever is most comfortable to you and best aligns with your goals. In particular, the front rack position will not allow as much "natural" trunk flexion as the back rack position. Thus, you will increase the demand of the knee extensors (quads) and decrease the demand placed on the hip extensors (glutes).
Using a step, as shown here, is a fantastic way to allow for MORE HIP FLEXION RANGE OF MOTION, thus forcing your GLUTES TO WORK HARDER. Try this if you're looking to increase the difficulty of your lunge