Mad scientist
It wouldn't make any sense that VLS was load factor sensitive. It would be as weird as if V2 was.
When you fly at VLS you know that you have a margin (arbitrarily determined) that should allow you "reasonable" manoeuverability without stalling. In the airbus PFDs, if you fly at VLS and pull up and bank steeply you will see Valpha prot and alpha max increasing towards a steady VLS, thereby indicating the effect of the load factor.
Otherwise VLS would increase above actual airspeed and that would be annoying because VLS is supposed to be a safe enough target airspeed.