Water-in-salt electrolytes with a surprisingly large electrochemical stability window of <= 3 V have revived interest in aqueous electrolytes for rechargeable lithium-ion batteries. However, recent reports of acidic pH measured in concentrated electrolyte solutions appear to be in contradiction with the suppressed activity of the hydrogen evolution reaction (HER). Therefore, the fundamental thermodynamics of proton reactivity in concentrated electrolyte solutions remains elusive. In this work, we have used density functional theory-based molecular dynamics (MD) simulations and the proton insertion method to investigate how the HER potential shifts in concentrated LiCl solutions under both acidic and alkaline conditions. Our results show that the intrinsic HER activity increases significantly with the salt concentration under acidic conditions but remains relatively constant under alkaline conditions. Moreover, by leverage over finite-field MD simulations, it is found that a determining factor for the HER activity is the Poisson potential of the liquid phase, which increases in concentrated electrolyte solutions with comparable values from both density functional theory and point-charge models.