Hi lawriem,
It is likely that you will need to create some custom font controls as your theme is overriding the default controls. To create a control just go to Settings > Google Fonts, give your font control a name, add the appropriate CSS selector and save the control. It will then become available in the customizer.
Here are some to get you started:
Navigation: #access div.menu ul li a
Page Title: #content h1.entry-title
Paragraphs: #content p
List Items: #content ul, #content ol
You generally need to have some knowledge of your themes CSS selectors to get the most out of this plugin. If you don’t have this knowledge then any basic developer should be able to give you a hand with it. Let me know how you get on. Cheers
Sunny