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

*it will change the geometry 

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

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