Any class can be any alignment.
That position on the moral spectrum suggests that your character believes to a certain extent in the value of moderation and utility. They prize outcome over method quite highly and tend to believe that the ends always justify the means. They probably value self-control as one of the highest of virtues and minding one's own business as the basis of all ethics and manners. But, in addition to those "neutral" minded ideas, they have leanings toward loyalty to a group that they favor over other groups for whatever reason, and they believe again that that group is justified in using whatever means necessary to protect and advance its own interests. They would probably feel that loyalty out of admiration for that group's ideas, but this could also be a case of simple proximity - loyalty to one's family or country where even if you think your group is misguided it's still your group. And while they still value balance, they tend to try to uphold that groups ideas whenever it doesn't conflict with their own sense of utilitarianism too strongly.
One interpretation of Dirty Harry's philosophy puts him at about this position on the alignment chart. This is also probably a decent version of James Bond's moral philosophy.
As a DM I'd consider it an interesting character concept compared to all the CN and CE leaning PC's I regularly see. Lawful is fun as a PC because that have a bit more complex emotional lives compared to someone that considers self-expression the be all end all of proper living. I'd could conceive of cool characters for this alignment positioning in almost anything but Cleric or Champion/Paladin, where I think a bit purer of a philosophical position is more interesting. Fighter, Hunter/Ranger, Rogue, Wizard, or Sorcerer all sound like a lot of fun.
