The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Replace In Subquery With Correlated Exists (modified query below): In many cases, an EXISTS subquery with a correlated condition will perform better than a non correlated IN subquery.

Optimal indexes for this query:

ALTER TABLE `item` ADD INDEX `item_idx_item_num_sa_item` (`item_num`,`sa_item`);
ALTER TABLE `item_w` ADD INDEX `item_w_idx_whse_code_item_num_repl_code` (`whse_code`,`item_num`,`repl_code`);
ALTER TABLE `item_w` ADD INDEX `item_w_idx_repl_code_whse_code` (`repl_code`,`whse_code`);

The optimized query:

SELECT
        DISTINCT l.item_num,
        l.repl_code 
    FROM
        item_w l 
    JOIN
        item i 
            ON l.item_num = i.item_num 
    LEFT JOIN
        item_w r 
            ON l.item_num = r.item_num 
            AND l.repl_code = r.whse_code 
    WHERE
        r.whse_code IS NULL 
        AND EXISTS (
            SELECT
                DISTINCT 1 
            FROM
                item_w AS item_w1 
            WHERE
                (
                    l.repl_code = item_w1.whse_code
                )
        ) 
        AND i.sa_item NOT LIKE 'Z%' 
    ORDER BY
        l.item_num,
        l.repl_code