When to include or exclude lone pair counting electrons according to Hückel's rules?
As written on Chemistry Libre Texts,


  Perhaps the toughest part of Hückel's Rule is figuring out which electrons in the compound are actually π electrons. Once this is figured out, the rule is quite straightforward.  π  electrons lie in p orbitals and  sp2 hybridized atoms have 1 p orbital each. So if every molecule in the cyclic compound is sp2 hybridized, this means the molecule is fully conjugated (has 1 p orbital at each atom), and the electrons in these p orbitals are the π electrons. 


In furan, there are two lone pairs, one in the sp2-orbital, and the other in the p-orbital. The latter is hence the set of π electrons. 

In the cyclopentadienyl anion, the lone pair is present in the p-orbital, as all the sp2-orbitals are involved in bonding.

Thus, π electrons and not just lone pairs are to be counted in Huckel's Rule.