Here's your problem:
(Lone pair in red, electrons participating in sigma bonds in blue)
Single atom orbitals like sp
2 and sp
3 are no longer very useful for analysis once you start considering molecular orbitals.
Rather than trying to assign the nitrogen's electrons to nitrogen atomic orbitals, consider the molecular orbitals of the pyridine system that nitrogen can participate in. The pyridine nitrogen is sp
2 hybridized, so it contributes 2 sp
2 orbitals to form a σ bond with each of the neighboring carbon atoms, one sp
2 orbital is left for the lone pair, and it contributes its unhybridized p orbital to the aromatic π system. The nitrogen contributes one valence electron to each of the σ bonding orbitals, one to the π system, and two to the nonbonding lone pair orbital. The core electrons remain in the 1s orbital.
Even in the case of the nonbonding lone pair orbital, though, if you calculated the energies of the various orbitals, you would find some contributions from other atomic orbitals.