A Program Change is its own MIDI message, it is not a CC.
Yes, you can use an iPad to select a song and have it send Program Changes to multiple attached keyboards. It can be done with either a MIDI routing app (like Keystage or Camelot Pro) or by a set list app (like Set List Maker with its MIDI IAP). Which app are you currently using for lyrics/chords? Check its manual to confirm whether/how it can be configured to send MIDI when you bring up a song, you may not need to buy another app at all.
You will need some way to connect both of your keyboards to your iPad. This can be done via either USB or 5-pin MIDI connections, and the exact connecting pieces you need will depend on whether your iPad has a lightning port or a USB-C. (There is also a wireless bluetooth option, e.g. CME's WIDI devices.)
As an aside, it is also possible to use the Fantom's Scenes such that, when you bring up an internal sound, it also changes the patch on an attached additional keyboard. You do this by including an EXTernal zone in the Scene. Since you don't want that external sound to play from the Roland's keys, you can set its key range to something beyond the playable keys on the keyboard. (There may be other ways to accomplish that goal as well.)
Mainstage does not run on iOS.