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Let $\zeta \left(s\right)$ be the Riemann zeta-function. If $t\ge 6.8$ and $\sigma >1/2$, then it is known that the inequality $\left|\zeta \right(1-s\left)\right|>\left|\zeta \right(s\left)\right|$ is valid except at the zeros of $\zeta \left(s\right)$. Here we investigate the Lerch zeta-function $L(\lambda ,\alpha ,s)$ which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters $\lambda =\alpha$ it is still possible to obtain a certain version of the inequality $|L(\lambda ,\lambda ,1-\overline{s})|>|L(\lambda ,\lambda ,s)|$.