It's not possible to update multiple tables in one statement, however, you can use the transaction to make sure that two UPDATE statements must be treated atomically.
You can also batch them to avoid a round trip like this.
BEGIN TRANSACTION;
UPDATE Table1
SET Table1.LastName = 'DR. XXXXXX'
FROM Table1 T1, Table2 T2
WHERE T1.id = T2.id
and T1.id = '011008';
UPDATE Table2
SET Table2.WAprrs = 'start,stop'
FROM Table1 T1, Table2 T2
WHERE T1.id = T2.id
and T1.id = '011008';
COMMIT;
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