The optimization process and recommendations:

1. Avoid Subqueries (query line: 7): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
2. 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.

Optimal indexes for this query:

ALTER TABLE `table3` ADD INDEX `table3_idx_subid` (`subid`);

The optimized query:

SELECT
        t1.id,
        t1.name,
        t2.subname,
        t2.refvalue 
    FROM
        table1 AS t1 CROSS APPLY (SELECT
            TOP 1 t2.subid,
            t2.subname,
            t3.refvalue 
        FROM
            table2 AS t2 
        INNER JOIN
            table3 AS t3 
                ON t2.subid = t3.subid 
        ORDER BY
            lastupdated DESC) AS t2