trying to a lag a column in SQLite

I have a table where rows represent individuals in a point in time. I am trying create a column (statusLag) with the lagged values of another column (status), like so:

workerID    timeVar     status      statusLag
---------------------------------------------
1           1           0           NULL
1           2           1           0
1           3           1           1
1           4           1           1
----------------------------------------------
2           3           1           NULL
2           4           0           1
2           5           1           0
2           6           0           1

What I have tried

Doing the following fails (leaves the column unchanged), and I can't understand why

ALTER TABLE myTable ADD COLUMN statusLag INTEGER;    

INSERT INTO myTable (statusLag)
    SELECT 
        (SELECT t2.status
            FROM myTable t2
            WHERE t2.workerID = t1.workerID AND
                  t2.timeVar < t1.timeVar
            ORDER BY t2.timeVar desc
            LIMIT 1)
    FROM myTable t1;

I almost achieve what I want by creating a new table:

CREATE TABLE myOtherTable
    (   'workerID'  REAL NOT NULL,
        'timeVar'   INTEGER NOT NULL,
        'statusLag' INTEGER,
        PRIMARY KEY('workerID', 'timeVar')
    )

INSERT INTO myOtherTable
SELECT t1.workerID, t1.timeVar, 
    (SELECT t2.status
        FROM myTable t2
        WHERE t2.workerID = t1.workerID AND
              t2.timeVar < t1.timeVar
        ORDER BY t2.timeVar desc
        LIMIT 1)
FROM myTable t1;

To achieve what I want, I would need to join myOtherTable with myTable. But this looks quite inefficient to me.

So my questions are: Why didn't my first attempt work? And How do I achieve what I want in a more efficient way?