I know some keyboards support apps that do what you are talking about, and I believe they are triggered from the tablet. Roland has it for sure. It would be interesting to hear how it's being done.
I am relying primarily on the keyboard to display text files, and I have the laptop for more challenging requests.
As an example, I had an unusually large number of off-the-wall requests last night, ranging from Raindrops Keep Falling On My Head, Higher and Higher, You Light Up My Life, Alley Cat, Remember Me, and others. I hadn't done some of these in years, but was able to pull up lyrics and chords in seconds. Then pick a style and go! I probably average 30 requests a night, most of which I know without seeing anything, but you have to be ready for anything.
Playing requests is a different ballgame from just running a pre-planned set list!