What are lone pairs and how are they represented in a Lewis dot diagram?

And ammonia is a go to example....

For nitrogen, #Z=7#, and thus there are 7 electrons, of which TWO are inner core, and not conceived to participate in intermolecular bonding....and FORMALLY there are 3 nitrogen based electrons in EACH of the #N-H#...the other electron that constitutes the bond derives from hydrogen....

And so we gots…#ddotNH_3#...and now the LONE PAIR is stereochemically active..electronic geometry is tetrahedral, and molecular geometry is trigonal pyramidal. And because the non-bonding nitrogen lone pair lies fairly close to nitrogen it compresses the #/_H-N-H# bond down from #109.5^@# to approx. #105^@# in ammonia.

On other hand, the lone pair explains the basicity of the ammonia molecule. Ammonium ion, #NH_4^+#, is a REGULAR tetrahedron.

And they are normally represented by a double-dot...alternatively we could try to draw the #sp_3# hybrid orbital...

Note that ammonia is a rather potent donor, and as well as binding to a proton #H^+#, it could bind to transition metal centres to give ammonia complexes....

Ammonium ion is more or less a regular tetrahedron...with #/_H-N-H=109.5^@#,,