How to UPDATE a SQLITE Column with an INNER JOIN on TWO FIELDS
In order to implement the join on two columns simultaneously, you can use an EXISTS predicate:

UPDATE Table_1 
SET Field3 = (SELECT Field3
              FROM Table_2
              WHERE (Table_1.Field1 = Table_2.Field1)
                AND (Table_1.Field2 = Table_2.Field2))
WHERE EXISTS (SELECT *
              FROM Table_2
              WHERE (Table_1.Field1 = Table_2.Field1)
                AND (Table_1.Field2 = Table_2.Field2));


If you are using version 3.15.0 or later, you can also take advantage of row value comparisons:

UPDATE Table_1 
SET Field3 =
    (SELECT Field3
     FROM Table_2
     WHERE (Table_1.Field1, Table_1.Field2) = (Table_2.Field1, Table_2.Field2))
WHERE (Field1, Field2) IN (SELECT Field1, Field2 FROM Table_2);