  For most values of parameters $\lambda$ and $\alpha$, the zeros of the Lerch
zeta-function $L(\lambda, \alpha, s)$ are distributed very chaotically. In this
paper we consider the special case of equal parameters $L(\lambda, \lambda, s)$
and show by calculations that the nontrivial zeros either lie extremely close
to the critical line $\sigma = 1/2$ or are distributed almost symmetrically
with respect to the critical line. We also investigate this phenomenon
theoretically.
