Question

When we consider lone pair having two electrons, why there is no electron-electron repulsion inside the lone pair?

Answer 1

Of course, there is repulsion undoubtedly, but the lone pair is in the same orbital with the electrons having opposite spins. Moreover, they are stabilized by pairing energy of the orbital.

Below is an example of oxygen. Oxygen has 6 valence electron and mostly uses two electrons to form covalent bonds.

Rest of the 4 valence electrons are in two separate orbitals and are paired up (thus providing stability). So, repulsion of lone pair is compensated.