So, no, anarchists are not right wing. They are left wing. Lawlessness is always left wing. Liberal is a synonym of licentious.
Then by your definition, excessive lawfulness (e.g., the Nazi state or Fascist Italy) is right-wing.
Or are both sides -- lawful and lawless -- both left-wing?
Although anarchy always finds it self contrary to government regulating policies(the dominant left wing position), anarchy can be left wing.
There is a difference between left wing anarchists and right wing anarchists. Right wing anarchists, such as militias and what not, oppose goverenmnet control to leave the individual more freedom and to act on his own accord.
Left wing anarchists or utopians, believe that the proletariot can share the means of production without government intervention. Although this is supposedly the aim of the communists, leftwing anarchists prefer to establish their aims without the "dictatorship of the proletariot".
A rational mind would probably rule out left wing anarchism, as a serious political establishment, with about 30 seconds worth of thought. Which is probably why communists never succeed in "withering away the state"
The extreme right of the spectrum would be the opposite. No control of the means of production. Some call it "Anarchy", whereas I prefer the term "Utopia".
The terms "Liberal" and "Conservative" engender confusion, especially to students of history, due to the evolution of the term "Liberal" from that of an anti-statist to that of a statist-socialist. While the term "Conservative" has such a defeatist connotation without context. To "conserve" what? The status quo of 1984, 1954, 1860, 1789?
It seems that in the era of mass "miscommunication", the only real use for the terms "Liberal" and "Conservative" is to enable politicians and pundits to engage in sophistry en masse.