The key idea of #"VSEPR"# is that non-bonding, and bonding electron pairs assume the shape of the Platonic solids.
#"Two electron pairs around a central atom, linear. "#
#"Three electron pairs around a central atom, trigonal planar."#
#"Four electron pairs around a central atom, tetrahedral."#
#"Five electron pairs around a central atom, trigonal bipyramidal."#
#"Six electron pairs around a central atom, octahedral. "#
I make no distinction as to whether the electron pairs are bonding or non-bonding. Non-bonding electron pairs are STILL stereochemically active, and the eventual structure is BASED on the parent platonic solid dictated solely by the number of electron pairs.
There should be many examples of #"vesper"# problems on these boards. I will give ONE example; that of ammonia, #NH_3#. There are 4 electron pairs around the central nitrogen: #3xxN-H# bonds, and ONE nitrogen centred lone pair. (Again, the nitrogen atom has 5 valence electrons, each hydrogen has 1 electron: 8 electrons, means 4 electron pairs.) Given the spiel above, the electron pairs arrange themselves around nitrogen in a tetrahedral array? Why?
Because, the electron pairs, both bonding and non-bonding, REPEL each other, and arrange themselves in a shape that minimizes the repulsion of electrons. For the nitrogen centre, this means that the electron pairs are distributed tetrahedrally with #/_H-N-H=109.5^@# to a first approximation. However, because the nitrogen lone pair is non-bonding, it lies closer to the nitrogen centre, and tends to compress #/_H-N-H# to approx #104-5^@#. The symmetry has descended from tetrahedral to trigonal pyramidal. But observe that we describe MOLECULAR symmetry on the basis of atoms, not electron pairs. We thus describe the geometry of ammonia as trigonal pyramidal.
And with #"VESPER"# simple electron counting can reliably predict the OBSERVED geometry of simple organic and inorganic molecules. This is a simple idea, and yet it yields very powerful results.