The brain can compensate for lag/latency up to a point. Church organ players often have to deal with >100ms of delay between pressing a key and hearing the note produced through those big pipes.
If you have an app which produces a sound when you tap on the screen, and there's a delay of say 70ms between tapping and sound being produced, it's easily possible to play in time with an external clock source, like a metronome, as long as the delay is fixed.
In the 1968 paper "Response time in man-computer conversational transactions" actions which occurred within 100ms the human input were perceived as instantaneous. In my experience this holds true with musical instrument apps, although one must first learn how much latency is present in order to compensate for it when synchronising with other clock sources.