I understand that the imidazole ring in histidine is aromatic. I also realize that it retains it's aromaticity when protonated. I am wondering why it is not mentioned at all in basic text books such as Lehninger? Also, across the web there are a number of places claiming that histidine isn't aromatic in all cases. Another reason I am a little confused is, if protonation doesn't harm the aromatic nature, then why is histidine such a weak base? Am I missing something?
This is one of my favorite charts demonstrating the complexity of amino acid properties:
Histidine is probably the most complicated amino acid in this regard (just compare how many circles it falls into). But don't undersell Cysteine and Methionine; those sulfurs exhibit some surprising behavior, especially when coordinated properly. Cysteine of course forming disulfide bonds, Methionine occasionally functioning as a methyl-transferase.
Biochemistry text books make some over simplifications because presenting the full messiness of these classifications is pretty confusing. Lehninger itself is the worst about this (and especially when presenting math). Voet and Voet is probably the most reliable about presenting this complexity. I still think Lehninger is a better teaching textbook overall (I was first taught Biochemistry from the 3rd edition), but I also recall spending a week being confused about a topic before someone pointed me at V&V and I realized Lehninger was oversimplified to the point of being wrong, in that case.
Books are not flawless.
Pyrolles have a weak basicity because of delocalization of the electron lone pair of nitrogen. It is the lone pair of nitrogen, in amines, which gives it basicity (Check Lewis bases and acids) .
In imidazole, the other nitrogen (N-2) has a free lone pair and does contribute to its basicity. As you pointed out before, imidazolium is a stable moiety and imidazole is much stronger base than pyridine.
But compared to lysine
The strong basicity of arginine is because of the guanidium group.
The imidazole ring in histidine is indeed aromatic. But an aromatic amino-acid is not usually defined as "an amino-acid with an aromatic ring". Rather, they are usually defined by common chemical properties, such as high absorption at 280nm, or better their common metabolic pathway.
Histidine as a stand-alone amino-acid is a weak base, but this is mainly due to the amino and acid groups shared with every amino-acid. The imidazole ring in itself has a neutral pKa.