Hi, can brain training web games (eg lumosity. Com) be harmful to kids above 3 years? Kids seem to love playing it - but is there any side-effect?

Above three? Do you mean above or below the age of three? Recent studies suggest that children under the age of two, really do not benefit from any video electronics. They can be too overstimulating. All children's tv programming should be limited to no more than one hour per day. I do not believe in having a tv in a child's room. You are not doing your kids a favor by exposing them too early to media.
Avoid the web. Normal and natural play is better than web based games. Talking, playing active games, telling stories to others and reading stories is the best brain training there is. Children are spending more than 7 hours per day in front of screens of all types. I do not believe that this is good - no matter what "brain training" it is supposed to be doing.