**Query 1**

Using a UNION should get you the results you want an not duplicate.

    SELECT l.[EmailAddress], e.[First_name]
    FROM _Job j with (nolock)
    INNER JOIN _Sent s with (nolock)
    ON j.JobID = s.JobID
    INNER JOIN _ListSubscribers l with (nolock)
    ON l.subscriberID = s.subscriberID
    INNER JOIN _EnterpriseAttribute e with (nolock)
    ON l.subscriberID = e._subscriberID
    WHERE s.EventDate < GetDate()
    AND e.Segment = 'Customer'
    AND j.EmailName NOT LIKE 'newsletter_%'
    AND l.ListID = 919445
    
    UNION
    
    SELECT l.[EmailAddress], e.[First_name]
    FROM _ListSubscribers l with (nolock)
    INNER JOIN _EnterpriseAttribute e with (nolock)
    ON l.subscriberID = e._subscriberID
    WHERE NOT EXISTS (SELECT * FROM _Sent WHERE _Sent.[subscriberID] = l.[subscriberID])
    AND e.Segment = 'Customer'
    AND l.ListID = 919445

**Warning:**

Depending on the size of your list this might time out. Unions take alot longer 

**Query 2**

    SELECT l.[EmailAddress], e.[First_name]
    FROM _Job j with (nolock)
    INNER JOIN _Sent s with (nolock)
    ON j.JobID = s.JobID
    INNER JOIN _ListSubscribers l with (nolock)
    ON l.subscriberID = s.subscriberID
    INNER JOIN _EnterpriseAttribute e with (nolock)
    ON l.subscriberID = e._subscriberID
    LEFT JOIN _Sent T ON l.subscriberID = T.subscriberID 
    WHERE s.EventDate < GetDate()
    AND e.Segment = 'Customer'
    AND j.EmailName NOT LIKE 'newsletter_%'
    AND l.ListID = 919445
    AND T.subscriberID IS NULL

**Query 3**

Personally, I would keep the queries separate as there are alot of joins here and it might not perform well as your database scales. 

Keeping the Assuming your 1st query is is DataExtensionA and your 2nd in DataExtensionB:

    SELECT
    EmailAddress
    ,First_Name
    
    FROM DataExtensionA
    
    UNION
    
    SELECT
    EmailAddress
    ,First_Name
    
    FROM DataExtensionB