I think your only option is to use a "mirroring" function to put the race on your TV. If your iPad is new enough, you can use Apple's Airplay Mirroring to put the race on your TV. Otherwise, you can use a 3rd party application called AirParrot.
One word of caution about AirParrot - it seems to be more geared towards businesses that want to put spreadsheets, presentations, etc up on a TV or monitor. Anything that moves seems to be a bit jerky. Their website has tips to optimize the viewing, but it doesn't completely get rid of the jerkiness.
Either way, you'll probably need to go to cyclingfans or steephill to find a streaming live link, then use either Airplay Mirroring or AirParrot to put the race on your TV. I'm not sure of any avenue where you will be able to get the race "on-demand."