What lines are you thinking on? Short of a BT Sport app in the TV Portal, any other potential tricks will rely on the BT Sport stream being available to a web browser and then a web stream to DLNA converter running on your PC. Wouldn't it be easier to use the BT Sport app and connect your computer to the TV (HDMI) or cast the screen to the TV (Chromecast/Apple TV)?
Do you have a suitable wire? Pre-Lightning, HDMI out of iPad was relatively easy; post-Lightning it needs a specific enable signal from the external adapter, and as far as I know that means an Apple iPad to HDMI adapter (at an Apple price).
When I looked into this (after upgrading my iPad) I decided to buy an Apple TV box (the cheapest model) instead of an HDMI adapter, and then cast the iPad screen to it. Not all apps support it though