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)