Line-commutated converter based high-voltage direct current (LCC-HVDC) systems may diminish the power grid strength, potentially precipitating static voltage stability issues. To maintain the required level of power grid strength while minimizing the total system cost, this paper proposes a coordinated expansion planning framework for multi-infeed LCC-HVDC (MI-HVDC) systems that explicitly incorporates generalized short-circuit ratio (gSCR) constraints. Specifically, the gSCR requirement is innovatively formulated as a semidefinite constraint, and the proposed framework is reformulated as a mixed-integer semidefinite programming (MISDP) model to guarantee the global optimality. Then, to address the computational intractability of the MISDP model, a generalized Benders decomposition (GBD)-based approach is employed for efficient solution. Time-domain simulations conducted in PSCAD/EMTDC demonstrate the effectiveness of the proposed framework in enhancing the voltage stability of MI-HVDC systems.