By offering a wide license-free spectrum, visible light communication (VLC) has emerged as a game-changing technology for networks beyond 5G. In this study, the multiple-input multiple-output (MIMO) technology is combined with a non-orthogonal multiple access VLC (NOMA-VLC) system to provide a reliable error-free high data rate network for multi-user scenarios. A generalized L-PPM modulated MIMO based multi-user NOMA-VLC system with M×N line-of-sight connections for each user is presented. Considering a practical scenario of imperfect successive interference cancellation, a novel closed form formulation of error probability for the proposed system is obtained. This study also includes a comprehensive analysis of two-user and three-user L-PPM modulated 2×2 MIMO-NOMA-VLC systems, and exact error probability expressions are derived. With the identical set of parameters, the L-PPM modulated MIMO-NOMA-VLC system totally outperforms the on-off keying modulated MIMO-NOMA-VLC system. As the number of photodetectors per user increases, the error probability of the considered system decreases. An L-PPM modulated 2×2 MIMO based three-user NOMA-VLC system offers the best performance at a power allocation co-efficient of 0.3. The simulation results validate the derived error probability expressions.