How to use parent table column inside subquery JOIN condition?
You may want to use EXISTS operator with Sub-query, but that serve in different scenarios, in your case moving NotificationQueue table down to the sub-query can make you to do join that your looking for, following is the example of same:

SELECT  op.OpportunityID, 
        op.Name AS [OpportunityName], 
        ua.Email AS OwnerEmail, 
        nt.NoteID, nt.Note,
        tks.TaskID, 
        tks.ActivityType, 
        ua.FirstName, 
        ua.LastName, 
        FORMAT(getdate(), 'M/dd/yyyy, hh:mm:ss tt') AS [datetime],
        lead.LeadID, lead.LeadName
FROM NotificationQueue nq
    INNER JOIN  Opportunity op WITH (NOLOCK) ON nq.RecordID = op.OpportunityID  
    INNER JOIN  UserAccount ua WITH (NOLOCK) on op.owner = ua.UserID
    LEFT JOIN   Note nt WITH (NOLOCK) ON op.OpportunityID = nt.RecordID AND nt.EntityID = 4 -- OPPORTUNITY
    LEFT JOIN   (
                SELECT  t.TaskID, t.TaskTypeID, 
                        t.OpportunityID, 
                        tt.Description AS [ActivityType] 
                FROM    Task t WITH(NOLOCK)
                        INNER JOIN TaskType tt ON t.TaskTypeID = tt.TaskTypeID
                ) tks ON op.OpportunityID = tks.OpportunityID

    LEFT JOIN   (
                SELECT  l.LeadID, 
                        l.Topic AS [LeadName], 
                        lo.AssociatedOpportunityId 
                FROM    LeadOpportunity lo WITH(NOLOCK)
                        INNER JOIN Lead l ON lo.ParentLeadId = l.LeadID
                WHERE l.Active = 1
                ) lead ON op.OpportunityID = lead.AssociatedOpportunityId

WHERE op.Active = 1 and nq.Processed = 'N'





As per comment, following is the example of last LEFT JOIN:

    OUTER APPLY (
                SELECT  l.LeadID, 
                        l.Topic AS [LeadName], 
                        lo.AssociatedOpportunityId 
                FROM    LeadOpportunity lo WITH(NOLOCK)
                        INNER JOIN Lead l ON lo.ParentLeadId = l.LeadID
                WHERE l.Active = 1 AND nq.RecordID = lo.AssociatedOpportunityId
                ) lead --ON op.OpportunityID = lead.AssociatedOpportunityId