Lib Left doesn’t really make sense. Libertarian means you want social AND economic freedom. Left according to the PC means you just want social freedom. Those are mutually exclusive.

• Libertarian means that you believe in individual liberty.
  
• Authoritarian means you believe the individual is subordinate to the collective.
• Left means you believe in economic justice.
• Right means you believe in hierarchical, authoritarian economic systems.

LibRight is the position that does not actually make sense, since authoritarian hierarchies and individual rights are at odds with each other. Thus LibRight ends up meaning "liberty for property owners, tyranny for everyone else."

“Left” in common usage means something roughly like you value social justice causes. Which typically (but, in fairness, not always) means you want the government to enforce your beliefs. Which again, is incompatible with libertarianism.

That is not what left means. What you are describing is liberals, who are AuthRight, just more centrist than conservatives.

On my scale: Y axis = regulation v freedom and X axis = social justice values v traditional values.

The scale is actually Y = collective vs individual and x axis = economic justice vs capitalism.