We studied native point defects as well as Eu and Dy ion doping in CaS by the simple DFT + Hubbard U method. The electronic properties and formation energies of native point defects and dopants have been discussed. We found the neutral S vacancy has the lowest energy of 0.62 eV under the Ca-rich limit. The Schottky pair is another dominant defect with a cost of 1.51 eV per defect site from S-rich to Ca-rich chemical potential limits. Our calculations on the thermodynamic transition levels confirm the experimental observed intrinsic blue two-peak broad band emissions stimulated by near-infrared range irradiation for undoped CaS. Both Eu and Dy show an energetic favorable trend to be substitutionally doped in the CaS lattice. All of the positive charge states of the Eu ion contribute localized recombination trapping level in the gap while having very deep donor transition levels. The neutral state of Dy contributes to the occupied 4f level localized 1.3 eV below the conduction band edge with very shallow donor type transition level (0/+) of 0.56 eV below the conduction band. All of the positive charge states of Dy have two shallow 5d levels with 0.4 and 0.6 eV below the conduction band. In this work, we further analyzed that the Dy dopant contributed deeper trap levels in the CaS materials that can store the electron carriers with more evenly, wider, and deeper range of levels distributed so that they lengthen the decay-time of the persistent luminescence. The related 980 nm photo-stimulated luminescence is actualized with the help of native defects like V-S(0), V-S(+), and STK- as relay centers for a possible up-converted luminescence. We also summarized a narrow doping limit energy which has been determined as 1.33 eV constantly in CaS independent to different chemical potential limits. This gives a solid theoretical reference for lanthanide ion doping experiments in CaS.