In this paper, we studied systematically the semileptonic decays B¯s→K(*)ℓ+ℓ− with l−=(e−,μ−,τ−) by using the perturbative QCD (PQCD) and the “PQCD+Lattice” factorization approach, respectively. We first evaluated all relevant form factors Fi(q2) in the low-q2 region using the PQCD approach, and we also took the available lattice QCD results at the end point qmax2 as additional inputs to improve the extrapolation of the form factors to the high-q2 region. We calculated the branching ratios and twelve other kinds of physical observables. From our studies, we find the following points: (a) for B¯s→Kl+l− decays, the PQCD and PQCD+Lattice predictions for branching ratios B(B¯s→Kl+l−), the ratios of the branching ratios RKeμ and RKμτ, and the longitudinal polarization asymmetry of the leptons PL agree well within errors; (b) the PQCD and PQCD+Lattice predictions for the CP-averaged branching ratio B(B¯s→K*μ+μ−) are (3.17−0.78+0.95)×10−8 and (2.48−0.50+0.56)×10−8 respectively, which agree well with the LHCb measured value (2.9±1.1)×10−8 and the light-cone sum rule prediction; (c) for the ratios RK*eμ and RK*μτ, 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 ACP of all considered decay modes, they are always very small as expected: less than 5% in magnitude; (e) for the angular observables P1,2,3 and P4,5,6,8′, our theoretical predictions for each kind of lepton are consistent within errors; (f) the theoretical predictions of the angular observables P3 and P6′ are less than 10−2 in size, but the magnitude of P1,2 and P4,5′ are larger than 0.2; and (g) the PQCD and PQCD+Lattice predictions of the binned values of all considered observables in the two q2 bins [0.1–0.98] GeV2 and [1.1–6] GeV2 generally agree with each other and are also consistent with the light-cone sum rule results within errors. We believe that above predictions could be tested by future LHCb and Belle-II experiments.