When throwing a jab is it necessary to step with the lead leg to add some power? I personally step with both feet for the sake of a strong base, also not to be vulnerable for an inside leg sweep to the lead leg. Should this be done?
do we need to step with the lead leg while throwing a jab to add some power?
No. A step is useful to get an opponent in range, but if they're already comfortably in range there's no need to step, and power comes from the legs twisting your hips and torso/shoulders into the punch - if you use some of that energy to move your whole body forward, and the body mechanics have to be compromised to power that move, it doesn't make the punch itself stronger - it makes it weaker than when the whole movement is dedicated to generating power.
I personally step with both feet for the sake of a strong base, also not to be vulnerable for an inside leg sweep to the lead leg.
When stepping, you do want to move both legs, but they might not move at exactly the same time. My Muay Thai school teaches to step the front foot first then slide the back foot in behind it. If that's done fast enough that you're not over-committing weight to the front foot, you avoid being particularly vulnerable to the front leg being swept, or worse perhaps - the front knee being kicked as it lands. The front foot should be kept light so you can kick or check/jam with it if needed.