The Chromecast works perfectly. BT do not now allow the sport app to be cast. I think that came into force last April. There is an explanation of it somewhere else on this forum. I have no problem casting anything else.
There is no BT sport app for LG televisions. If you try to use the btsport.com website on a LG tv you are told to update the browser, which you can't do.
So the only way to get the picture on to a LG tv is to cast it from a mobile device which is using the website.