  We study Leggett-Garg inequality (LGI) of a two level system (TLS) undergoing
non-Hermitian dynamics governed by a non-linear Bloch equation (derived in J.
Phys. A: Math. Theor. 54, 115301 (2021)) across a PT-transition. We present an
algebraic identification of the parameter space for the maximum violation of
LGI (in particular $K_{3}$). In the PT-symmetric regime the maximum allowed
value for $K_{3}$ is always found to be greater than the quantum bound
(L\"{u}ders bound) of $3/2$ but it does not reach the algebraic maximum of
$K_{3}=3$ in general. However, in the limit where PT-symmetry breaking
parameter approaches the exceptional point from the PT-symmetric side, $K_{3}$
is found to asymptotically approach its algebraic maximum of 3. In contrast,
the maximum value of $K_{3}$ always reaches its algebraic maximum in the
PT-broken phase $i.e.$ $K_{3}\rightarrow 3$. We find that (i) the speed of
evolution (SOE) must reach its maximum value (in the parameter space of initial
state and the time interval between successive measurements) to facilitate the
value of $K_{3} \rightarrow 3$, (ii) together with the constraint that its
minimum value must run into SOE equals to zero during the evolution of the
state. In fact we show that the minimum speed of evolution can serve as an
order parameter which is finite on the PT-symmetric side and identically zero
on the PT-broken side. Finally, we discuss a possible experimental realization
of this dynamics by quantum measurement followed by post-selection procedure in
a three level atom coupled to cavity mode undergoing a Lindbladian dynamics.
