Question

How does adding a lone pair affect the position of existing atoms and lone pairs?

Answer 1

You simply can't "add" a lone pair of electrons to a molecule or polyatomic ion. The substance will simply have all the electrons the atoms came with. 

Lone pairs on the central atom will change the geometry about the central atom according to the rules of VSEPR theory. Lone pairs will also distort the geometry predicted by VSEPR theory. Lone pairs are not "centered" between to atoms, but tend to "wrap around" the central atom and force the bonding pairs of electrons closer together, thus, causing the distortion in the geometry. 

VSEPR == valence shell electron-pair repulsion. It's all about the repulsion of the valence electron pairs. They get as far apart as possible, and that establishes the electron-pair geometry. From the electron pair geometry we get the molecular geometry and bond angles. 

#electron pairs ..... electron pair geom ..... molecular geometry ........ bond angles 
------------------ …. ----------------------- ….------------------------- …... ----------------- 
2 .......................... linear............................ linear .............................. 180 
3 (no lone pairs) .. trigonal planar ............. trigonal planar ................ 120 
3 (one lone pair) .. trigonal planar ............. bent .......................…...... 120 (less than) 
4 (no lone pairs) .. tetrahedral ................... tetrahedral ............…....... 109.5 
4 (one lone pair) .. tetrahedral ................... trigonal pyramidal .......... 109.5 (or less) 
4 (2 lone pairs) .... tetrahedral ................... bent ......................…....... 109.5 (or less) 
5 (no lone pairs) .. trigonal bipyramidal ......trigonal bipyramidal ....... 90 and 120 
5 (one lone pair) .. trigonal bipyramidal ..... see-saw ........................... 90 and 120 
and so on

Answer 2

*it will change the geometry 

changes postion of the lone pairs and atoms so that they are furthest apart