Hey this thread is a mess, but I'll try to contribute!
I think you're confused or the achiever is unclear. Being part of the plane of the ring, it should refer to being part of the planar configuration of the conjugated ring? There are 2 places a lone pair like that can occupy. The plane of the ring, or in the p-orbital. pi bond overlap.
The lone pair is part of the ring and NOT part of the pi-bond/ p-orbital overlap.
Look at figure 2.
No formal charges, so no hyrdogen on it. The hybridization is sp2.
All sp2 hybridization will take the 1 s orbital and 3 p orbitals and translare them into 4 oribtals. As a result, there will be 3 sp2 orbitals of course, and the 4th oribtal will be the left over p(z) orbital that WASN'T hybridized. So its just there hoping to be filled.
p> _ _
_
s > _
turns into
sp2> _ _ _ +
_
The C-N and C-N bonds will occupy the first 2 sp2 orbitals.
The lone pair will fill the 3rd sp2 orbital and
there's nothing in the p-oribtal; its empty. So it won't contribute to the pi electon count.
Only if all 3 sp2 orbitals are filled can your lone pair be put in the extra p-orbital of an sp2 atom. So say it had another lone pair on that. Then that will fill the open p-orbital since all 3 sp2 orbitals are already filled by the C-N, C-N, and first lone pair. So in figure 2, the lone pair IS PART OF THE PLANAR ring, but not part of the pi bond overlapping. I think the Achiever's explanations might be unclear? You have 10 pi electrons which follows 4n+2.
Usually inside lone pair will be part of the ring, but don't go by that.
Don't go by the double bond to Nitrogen thing either. Use my logic, its the truth
🙂 Or look it up, cus this is how textbooks explain it.