no, because iOS disables to run a app which captures the screen if the app is closed. so you're only able to get such a app if you develop it by your own (which would be against the guidelines from apple). On the official app store you would not get such a app. maybe if you get another App Store - but this isn't confirm to apples principles and your device would lose warrante.
But you could by the Apple Digital AV Adapter and try to capture the html with for example Blackmagicdesign Intensity Shuttle Thunderbolt for 239$. So there is no cheap way.