We have systematically studied the structural and physical properties of the superconducting hydrated Li_x(H₂O)_yTaS₂ (0.22 ≤ x ≤ 0.58, y ≈ 0.86). The powder X-ray diffraction patterns suggest that all the samples are single-phase compounds, and the crystal structure is similar to that of 2H-TaS₂ (P6₃/mmc). The transition temperature to superconductivity shows a dome-shape dependence on the lithium content x with a maximum T_c of 4.6 K for x ≈ 0.42, which is larger than in corresponding optimally doped 2H-TaS₂ superconductors without water or organic intercalants (T_c ∼ 4.2 K). There are no signs of a charge-density-wave formation in hydrated Li_x(H₂O)_yTaS₂. While our magnetic data indicate a rather strongly type-II behavior, heat-capacity measurements reveal, like in other 2H-TaS₂-type compounds, a reduced discontinuity ΔC_e/γT_c ≈ 0.8 at T_c, which is smaller than the standard BCS value 1.43. From the corresponding Sommerfeld constants γ and Debye temperatures Θ_D we can derive the parameter describing the electron–phonon coupling λ_ep and the electron density of states DOS(E_F) at the Fermi level as functions of x. While the variation of the DOS(E_F) is consistent with that of T_c, indicating that the lithium intercalation is tuning T_cvia changing the DOS(E_F) in 2H-Li_x(H₂O)_yTaS₂, the simultaneous changes of λ_ep and Θ_D may also play a certain role.