Yeah, I see your dilemma. Try logging into ESPN via LG's web browser see if that works.
When googling your issue this seems to be an ESPN & LG problem. I guarantee that you can watch most stuff via airplay except ESPN.
Yeah, LG and ESPN don't have a deal to have the ESPN app on LG TVs, and the ESPN app onobile devices doesn't recognize the TV as an eligible casting destination. I get that it's business, but it's still dumb.
Had me dumbfounded when I set up my G3 and found out quickly that I need to cop another Chromecast.