If I understand your query correctly, you are facing issues with Lato and Myriad Pro fonts not displaying correctly, right?
Well, could you please upload your site to Business Catalyst as a test and see if the problem remains same?
Also Can you please follow the instructions mentioned in this post - why was yesterday the typefont Lato displaying?
Let me know if it helps.
Can you check a setting in your Site Properties and try publishing the site after you change it?
I've heard that at times that seems to fix errors with diacritics. (not sure why, but if it works, it works right?).