The optimization process and recommendations:

1. Avoid Selecting Unnecessary Columns (query line: 2): Avoid selecting all columns with the '*' wildcard, unless you intend to use them all. Selecting redundant columns may result in unnecessary performance degradation.
2. Avoid Selecting Unnecessary Columns (query line: 23): Avoid selecting all columns with the '*' wildcard, unless you intend to use them all. Selecting redundant columns may result in unnecessary performance degradation.
3. 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.
4. Use UNION ALL instead of UNION (query line: 22): Always use UNION ALL unless you need to eliminate duplicate records. By using UNION ALL, you'll avoid the expensive distinct operation the database applies when using a UNION clause.

Optimal indexes for this query:

ALTER TABLE `agents` ADD INDEX `agents_idx_lagentid` (`lAgentID`);

The optimized query:

SELECT
        p.*,
        a1.*,
        a2.szFirstName AS a2FirstName,
        a2.szLastName AS a2LastName,
        a2.szEmail AS a2Email,
        a3.szFirstName AS a3FirstName,
        a3.szLastName AS a3LastName,
        a3.szEmail AS a3Email 
    FROM
        propertySummary p 
    LEFT OUTER JOIN
        agents a1 
            ON p.lAgentID = a1.lAgentID 
    LEFT OUTER JOIN
        agents a2 
            ON p.lAgentID2 = a2.lAgentID 
    LEFT OUTER JOIN
        agents a3 
            ON p.lAgentID3 = a3.lAgentID 
    UNION
    SELECT
        p.*,
        a1.*,
        a2.szFirstName AS a2FirstName,
        a2.szLastName AS a2LastName,
        a2.szEmail AS a2Email,
        a3.szFirstName AS a3FirstName,
        a3.szLastName AS a3LastName,
        a3.szEmail AS a3Email 
    FROM
        propertySummary p 
    RIGHT OUTER JOIN
        agents a1 
            ON p.lAgentID = a1.lAgentID 
    RIGHT OUTER JOIN
        agents a2 
            ON p.lAgentID2 = a2.lAgentID 
    RIGHT OUTER JOIN
        agents a3 
            ON p.lAgentID3 = a3.lAgentID