Yep, Splashtop Remote is also available on the iPhone, so you could play LR (or whatever else) lessons on your iPhone too.
As for the native app we are developing, it will be for the iPad only, at least in the beginning. I don't feel that a phone's screen is big enough for a baby/young child, that's why iPad is our higher priority. No doubt one day we'll get around to modifying it for the iPhone though.
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http://www.splashtop.com/remote )