Ammonia is clearly a neutral molecule and its Lewis structure reflects this. Each hydrogen shares 1 electron from the #N-H# bond to balance its nuclear charge. The nitrogen atom has 2 inner core electrons, gets 3 electrons from the #N-H# bonds, and gets 2 electrons from the formal lone pair: #2+3+2=7e^-#. These 7 electrons are precisely balanced by the 7 protons in the nitrogen nucleus (which nuclear charge must be there if it is a nitrogen atom).
Now when ammonia is quaternized, the nitrogen is conceived to have a half share only of the the electrons in the #4xxN-H# bonds. So thus #4# electrons, + #2# inner core electrons, do not balance the #+7# nuclear charge. Nitrogen, in ammonium ion is formally cationic. This is consistent with the stoichiometric equation.
Note that all of the #N-H# in ammonium are equivalent; the #NH_4^+# cation is a tetrahedron. What hybridization would we assign the free base and the acid?
