I guess itīs a never-ending depate:
Some will argue children have every right to be in the MLL, scream, run around and itīs perfectly acceptable to inconvenience other pax.
Others will argue that the MLL is intended to be a quiet oasis from the terminal and is not designed for children and if anyone brings children into a lounge they need to behave accordingly (i.e. be quiet or leave the lounge).
Iīve met perfectly well behaved children (i.e. parents told children to be quiet and prepared by giving the kid a book or an ipad) while most parents unfortunately seem to fall into category 1.