Hello Jenna,
Thanks for writing in! To change the font style of you mailchimp submit button, please add the following css code in the customizer, Appearance > Customize > Custom > CSS
.x-subscribe-form input[type="submit"]{
font-family: "Lato", sans-serif;
font-style: normal;
font-weight: 300;
}
Hope this helps. Please let us know how it goes.