Earth-moon L1 Lagrange point stability

I have read that a satellite orbiting the L1 Lagrange point of the Earth-moon system is an unstable orbit and a tiny nudge in the right direction can send the satellite towards the Earth or the moon. See, for example, Is lagrange point L1 stable?. Is there a formula to calculate the 'tiny nudge' force if the satellite mass is m? Also, I suspect that the satellite will not fall like a stone into the Earth or the moon but will follow a spiral path into either body. Am I right? If yes, I suppose it won't be easy to pinpoint the place on Earth or the moon where the satellite will crash into.