This doesn't really have anything to do with the "look up" fields. You can specify a font for text in a field in two ways: You can select a font and for a field while in layout mode or you can select the text in a field while in browse mode and specify a font and size. This is also true for styles and text colors as well.
Styles applied to the field in layout mode will be superseded by styles applied to the text inside the field for any records where this has been done.
Here's a simple auto-enter calculation that can be set up in field options that strips out any such formatting applied to the text in the field:
TextFormatRemove ( self ) /* with earlier versions of filemaker use the actual field name in place of 'self' */
If you've never done this before, go to Manage | Database | Fields and double click the field definition for the field in the look up table.
Click the auto-enter tab and then choose the calculation option.
After entering the calculation, clear the "Do not replace existing value..." check box.
To strip out the formatting in your look up tables, You can use the textFormatRemove(fieldname) expression in a Replace Field contents operation on each such field.