Is there a property that I can add to a column so that it converts its value to lowercase? Instead of doing it for every single value through PHP?
Yes, but don't do it.
If you want exclusively lowercase characters in a column, convert them when you insert (or update) them.
If you need a column to be case insensitive in comparisons, use a case insensitive collation (which are used by default in e.g. utf8 columns)
You could probably do it through a trigger that fires on insert or update. Myself, I'd rather just create a view that has a lower-case version of the column in question. The SQL for the view might look like
SELECT ID, LOWER(MY_COLUMN) AS MY_COLUMN_LOWERCASE
FROM MY_TABLE;