  In this paper, we studied systematically the semileptonic decays $\bar{B}_s
\to K^{(*)} \ell^+ \ell^-$ with $l^-=(e^-,\mu^-,\tau^-)$ by using the
perturbative QCD (PQCD) and the "PQCD+Lattice" factorization approach,
respectively. We first evaluated all relevant form factors $F_i(q^2)$ in the
low $q^2$ region using the PQCD approach, and we also take the available
Lattice QCD results at the end point $q^2_{max}$ as additional inputs to
improve the extrapolation of the form factors to the high $q^2$ region. We
calculated the branching ratios and other twelve kinds of physical observables.
From our studies, we find the following points: (a) for $ \bar{B}_s \to K l^+
l^-$ decays, the PQCD and "PQCD+Lattice" predictions for branching ratios (BRs)
${\cal B}(\bar{B}_s \to K l^+ l^-)$, the ratios of the BRs $R_K^{e\mu}$ and
$R_K^{\mu\tau }$, and the longitudinal polarization asymmetry of the leptons
$P_L$ agree well within errors; (b) the PQCD and "PQCD+Lattice" predictions for
the CP averaged branching ratio ${\cal B}(\bar{B}_s \to K^* \mu^+ \mu^-)$ are
$(3.17^{+0.95}_{-0.78})\times 10^{-8}$ and $(2.48^{+0.56}_{-0.50})\times
10^{-8}$ respectively, which agree well with the LHCb measured value $(2.9\pm
1.1) \times 10^{-8}$ and the light-cone sum rule (LCSR) prediction; (c) for the
ratios $R_{K^\ast}^{e\mu }$ and $R_{K^\ast}^{\mu \tau}$, the PQCD and
"PQCD+Lattice" predictions agree well with each other and have a small error
less than $10\%$; (d) for the direct CP asymmetries ${\cal A}_{CP}$ of all
considered decay modes, they are always very small as expected: less than $5\%$
in magnitude; and (e) for the angular observables $P_{1,2,3}$ and
$P^\prime_{4,5,6,8}$ , our theoretical predictions for each kind of lepton are
consistent within errors. We believe that above predictions could be tested by
future LHCb and Belle-II experiments.
