LIMIT is not allowed when the UPDATE has joins. You can however move the join and the LIMIT inside a subquery and then join back to the table to be updated using the primary or a unique key. This is allowed:
UPDATE table1 AS upd
JOIN
( SELECT t1.pk
FROM table1 AS t1
JOIN
table2 AS t2 ON t2.col = t1.col
WHERE t1.row2 LIKE '%something%'
-- ORDER BY some_expressions
LIMIT 1
) AS sel
ON sel.pk = upd.pk
SET
upd.row1 = 'a value' ;
It's also good to use ORDER BY with LIMIT. Otherwise an arbitrary row will be selected.
If you want to update both tables (one row from each one), then you just need to join the derived table to the second table, too:
UPDATE
( SELECT t1.pk AS pk1, -- The PK columns
t2.pk AS pk2 -- of each table
FROM table1 AS t1
JOIN
table2 AS t2 ON t2.col = t1.col
WHERE t1.row2 LIKE '%something%'
-- ORDER BY some_expressions
LIMIT 1
) AS sel
JOIN table1 AS upd1 ON sel.pk1 = upd1.pk -- join table1
JOIN table2 AS upd2 ON sel.pk2 = upd2.pk -- join table2
SET
upd1.row1 = 'a value',
upd2.roww = 'some other value' ;
Test at rextester.com