Character sets & collations, not my favorites, but they DO work:
mysql> SET NAMES latin1;
mysql> SELECT 'lápiz' LIKE 'lapiz';
+-----------------------+
| 'lápiz' LIKE 'lapiz' |
+-----------------------+
| 0 |
+-----------------------+
1 row in set (0.01 sec)
mysql> SET NAMES utf8;
mysql> SELECT 'lápiz' LIKE 'lapiz';
+-----------------------+
| 'lápiz' LIKE 'lapiz' |
+-----------------------+
| 1 |
+-----------------------+
mysql> SET NAMES latin1;
mysql> SELECT _utf8'lápiz' LIKE _utf8'lapiz' ;
+---------------------------------+
| _utf8'lápiz' LIKE _utf8'lapiz' |
+---------------------------------+
| 1 |
+---------------------------------+
A nice chapter to read in the manual:Character Set Support