Yes, Lights Out is fully free on MentalMath and playable without any registration.
Turning off the lights so they all go dark develops logical thinking and the ability to plan ahead. A child learns to predict the result of each tap in advance.
Children can start with smaller boards from age 6, while larger grids are more engaging for older kids.
Yes, it works on phones, tablets, and computers. Tapping the lights off is especially comfortable on a touchscreen.
About 5-10 minutes a day and a few solved puzzles are plenty to train logic. Keep going as long as your child stays curious.