The optimization process and recommendations:

1. Mixed Order By Directions Prevents Index Use (modified query below): The database will not use a sorting index (if exists) in cases where the query mixes ASC (the default if not specified) and DESC order. To avoid filesort, you may consider using the same order type for all columns. Another option that will allow you to switch one direction to another is to create a new reversed "sort" column (max_sort - sort) and index it instead.

The optimized query:

SELECT
        `lpsi`.`listing_product_id` 
    FROM
        `m2epro_listing_product_instruction` AS `lpsi` 
    LEFT JOIN
        `m2epro_processing_lock` AS `pl` 
            ON pl.object_id = lpsi.listing_product_id 
            AND model_name = 'M2ePro/Listing_Product' 
    WHERE
        (
            lpsi.component = 'ebay'
        ) 
        AND (
            pl.id IS NULL
        ) 
    GROUP BY
        `lpsi`.`listing_product_id` 
    ORDER BY
        MAX(lpsi.priority) DESC,
        MIN(lpsi.create_date) ASC LIMIT 10