Say I'm a count or a duke in the Middle Ages. What would my day consist of, what would I do in my free time, and what kind of relationship would I have with vassals and serfs? What about my courtiers?
I understand your question well enough and there are far better people than I to answer it but technically neither title would be considered lesser lords. Dukes are in fact in most cases the highest noble title whereas count is a "mid level" nobleman. Knights, Hereditary Knights, Baronets and possibly Barons might be considered lesser lords.