In SQL Server, I can do something like this:
SQL Server
UPDATE tbl1 SET col2 = tbl2.col2 FROM table1 tbl1 INNER JOIN table2 tbl2 ON tbl1.col1
This works for sqlite:
UPDATE tbl1 SET col2 = (SELECT col2 FROM tbl2 WHERE tbl2.col1 = tbl1.col1)