“My liege, how art thou on this fine evening?” Is from what era of speech?

Elizabethan era.

Explanation:

Words like "liege" and "thou" were commonly used in the Elizabethan period. At that time the language used to be more formal compared to the way we speak today, for this reason, it is common that in books of the Elizabethan era, we can see the characters talking casually and using these words. Shakespeare, who was a great author of that time, used this type of speech with great recurrence.