What will be the optimal fps for such a game to run without lags on mobile devices? Higher fps means less time for game logic to be executed each frame?
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A lag free experience depends on the performance of your device, your game logic, assets and other resources. You have to profile it.
Some devices can pull of lag-free, solid 60fps or even 120fps, others struggle even at 30fps.
I recommend to target 60fps. 30fps are seen as a minimum, but 60fps assure a more decent, fluid experience.
And yes, higher fps means less time for game logic to be executed in each frame to achieve 60fps.
Game logic is computed on the CPU. If it cannot be computed in 1/60secs, the blitting/rendering will get stalled and has to postpone the new rendering frame.
You have to test your game on various devices, if it can pull off 60fps.
The game fps has to be in sync with the screen/display refresh rate to get the best result. Most, if not all, mobile displays have a refresh rate of 60Hz. If your game has only 30fps, it will produce double-frames like in the cinemas. This offers a better experience, as movies have a guaranteed frame rate, but may not your game.
Where are the hardware Sprites when you need them? Guaranteed frame-rates or timed actions down to a single instruction? I guess back to the C64 and arcade machines then 
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