Lattice-reduction-aided precoding (LRP) provides near-capacity rates with the use of low-complexity linear receivers for coded multiple-input multiple-output (MIMO) systems. However, a large amount of feedback in the feedback for an integer or binary precoding matrix has been a bottleneck in its implementation. In this paper, we propose a codebook-based LRP scheme for limited-feedback coded MIMO systems. The proposed LRP scheme follows the fundamentals of the previous LRP scheme that employed multilevel binary coset coding so that the precoding matrix is binary. In the proposed LRP scheme, the conventional precoding matrix obtained from the Lenstra-Lenstra-Lovasz algorithm is modified to specific forms that are predefined in a codebook set. The new precoding matrix is selected such that the lower bound on the capacity is maximized for a given codebook set, while the codebook set is designed offline such that the upper bound of the average capacity loss induced by the limitation on the codebook size is minimized. The simulation results show that the proposed LRP scheme nearly achieves the achievable rate of the conventional LRP scheme with a greatly reduced amount of feedback.