Transition metal dichalcogenides (TMDCs) represent a well-known material family with diverse structural phases and rich electronic properties; they are thus an ideal platform for studying the emergence and exotic phenomenon of superconductivity (SC). Herein, we propose the existence of tetragonal TMDCs with a distorted Lieb (dLieb) lattice structure and the stabilized transition metal disulfides (MS2), including dLieb-ZrS2, dLieb-NbS2, dLieb-MnS2, dLieb-FeS2, dLieb-ReS2, and dLieb-OsS2. Except for semiconducting dLieb-ZrS2 and magnetic dLieb-MnS2, the rest of metallic dLieb-MS2 was found to exhibit intrinsic SC with the transition temperature (TC) ranging from ∼5.4 to ∼13.0 K. The TC of dLieb-ReS2 and dLieb-OsS2 exceeded 10 K and was higher than that of the intrinsic SC in the known metallic TMDCs, which is attributed to the significant phonon-softening enhanced electron-phonon coupling strength. Different from the Ising spin-orbit coupling (SOC) effect in existing non-centrosymmetric TMDCs, the non-magnetic dLieb-MS2 monolayers exhibit the Dresselhaus SOC effect, which is featured by in-plane spin orientations and will give rise to the topological SC under proper conditions. In addition to enriching the structural phases of TMDCs, our work predicts a series of SC candidates with high intrinsic TC and topological non-triviality used for fault-tolerant quantum computation.