  The Standard Model gauge group can be extended with minimal matter content by
introducing anomaly free U(1) symmetry, such as $L_e-L_{\mu}$ or
$L_e-L_{\tau}$. If the neutral gauge boson corresponding to this abelian
symmetry is ultra-light, then it will give rise to flavor-dependent long-range
leptonic force, which can have significant impact on neutrino oscillations. For
an instance, the electrons inside the Sun can generate a flavor-dependent
long-range potential at the Earth surface, which can suppress the $\nu_{\mu}
\to \nu_e$ appearance probability in terrestrial experiments. The sign of this
potential is opposite for anti-neutrinos, and affects the oscillations of
(anti-)neutrinos in different fashion. This feature invokes fake CP-asymmetry
like the SM matter effect and can severely affect the leptonic CP-violation
searches in long-baseline experiments. In this paper, we study in detail the
possible impacts of these long-range flavor-diagonal neutral current
interactions due to $L_e-L_{\mu}$ symmetry, when (anti-)neutrinos travel from
Fermilab to Homestake (1300 km) and CERN to Pyh\"asalmi (2290 km) in the
context of future high-precision superbeam facilities, DUNE and LBNO
respectively. If there is no signal of long-range force, DUNE (LBNO) can place
stringent constraint on the effective gauge coupling $\alpha_{e\mu} < 1.9
\times 10^{-53}~(7.8 \times 10^{-54})$ at 90% C.L., which is almost 30 (70)
times better than the existing bound from the Super-Kamiokande experiment. We
also observe that if $\alpha_{e\mu} \geq 2 \times 10^{-52}$, the CP-violation
discovery reach of these future facilities vanishes completely. The mass
hierarchy measurement remains robust in DUNE (LBNO) if $\alpha_{e\mu} < 5
\times 10^{-52}~(10^{-52})$.
