the walking lunge is a great exercise to increase strength, endurance, stability, and balance unilaterally but unfortunately, most people make mistakes when they perform it. one of the main reasons we do lunge is, as mentioned, to challenge stability and that is possible by using only one leg(unilateral) instead of two(bilateral). also, the benefits of strength come when you add more resistance to the leg which is more when you use one leg at a time. but if you are just starting out with this exercise, it is alright to use both legs until you gain more experience but make sure your gait is the way i mentioned in this video so you do not get injured.