Gimbal lock is inherent to Euler angles and is not a matter of conversion between systems. It happens when an axis gets rotated exactly onto another axis, causing later rotations to become undefined.
The technique of adding parent and child angles is wrong because it simply does not work. It may work in certain special cases, such as only one axis being used. But in general it will fail.
The technique of adding parent and child angles is wrong because it simply does not work. It may work in certain special cases, such as only one axis being used. But in general it will fail.