Although La(2)Cu(1-x)Li(x)O(4) [Li-LCO] differs from La(2-x)Sr(x)CuO(4) [Sr-LCO] in many ways (e.g., the absence of metallic transport, high-Tc superconductivity, and incommensurate antiferromagnetic correlations), it has been known that certain magnetic properties are remarkably similar. The present work establishes the detailed bulk magnetic phase diagram of Li-LCO (0 <= x <= 0.07), which is found to be nearly identical to that of lightly-doped Sr-LCO, and therefore extends the universality of the phase diagram to hole-doped but nonsuperconducting cuprates.