Field sequential color liquid crystal displays (FSC-LCDs) are promising for applications needing high brightness and high resolution because removing color filters brings three times the light efficiency and spatial resolution. In particular, the emerging mini-LED backlight introduces compact volume and high contrast. However, the color breakup severely deteriorates FSC-LCDs. Concerning color breakup, various 4-field driving algorithms have been proposed at the cost of an additional field. In contrast, although 3-field driving is more desired due to fewer fields used, few 3-field methods that can balance image fidelity and color breakup for diverse image content have been proposed. To develop the desired 3-field algorithm, we first derive the backlight signal of one multi-color field using multi-objective optimization (MOO), which achieves a Pareto optimality between color breakup and distortion. Next, considering the slow MOO, the MOO-generated backlight data forms a training set to train a lightweight backlight generation neural network (LBGNN), which can produce a Pareto optimal backlight in real-time (2.3 ms on GeForce RTX 3060). As a result, objective evaluation demonstrates a reduction of 21% in color breakup compared with currently the best algorithm in color breakup suppression. Meantime, the proposed algorithm controls the distortion within the just noticeable difference (JND), successfully addressing the conventional dilemma between color breakup and distortion for 3-field driving. Finally, experiments with subjective evaluation further validate the proposed method by matching the objective evaluation.