The aim of this work is to provide energy level calculations among the lowest 71 levels arising out of 1$s^2$ and 1$snl$ ($n ≤ 6, l ≤ (n − 1)$) configurations of He-like lithium. The calculations are carried out through the relativistic configuration interaction approach and the second-order many-body perturbation theory implemented in the flexible atomic code. We provide accurate calculations of energy levels, lifetimes, wavelengths, weighted oscillator strengths and radiative rates for the allowed ($E1$) transitions of He-like lithium. We have also considered relativistic effects by incorporating quantum electrodynamics and Breit corrections. The radiative lifetimes are reported for all the calculated levels. The present results are in good agreement with the previous results in literature (theoretical and experimental data). Several new energy levels and wavelengths were found out where no other theoretical or experimental results are available. We expect that our extensive calculations will be useful to experimentalists for identifying the fine-structure levels.