You can accomplish this with jQuery. See here for an example on how to add it to SharePoint.
Go to your task list, then on the ribbon, click on List > Customize List > Form web parts > Default Edit Form.
Add a Content Editor web part and in the Content Link box, set a link to a js file that you will put in a document library of your choice (eg. SiteAssets library).
Inside this js file, put this code:
$(this).val() == 'Late' ? 'red' : ''