The spectroscopic properties of Li atoms and Li-like Ca and Ti ions in the plasma environment are investigated using a relativistic coupled-cluster (RCC) method. Assuming that the plasma is of low density and very hot, we consider the Debye model with two approximations to account for the screening effects: (i) in the nuclear potential alone and (ii) in both the nuclear and the electron-electron interaction potentials. Also, calculations for the energies and the lifetimes of the atomic states are carried out for plasma-free systems to check their accuracy, after which they are investigated in the plasma environment. It is observed that screenings in the electron-electron interaction potentials stabilize the systems more than when the screenings are present only in the nuclear potential. Similarly, the blue and red shifts in the Delta n = 0 and Delta n not equal 0 transition lines (with the principal quantum number n) of the Li-like ions observed in the (i) approximation are altered in the (ii) approximation. The level crossings among the energy levels are observed for large screening effects and are found to be prominent in the states of higher orbital angular momentum. The lifetimes of many low-lying states of the allowed transitions are estimated by considering different plasma screening strengths.