I suppose we all have a definition of what makes someone a lady, but in Regency era England, where many of my stories are set, there are specific rules for when a woman may be addressed as Lady.
If a woman is a daughter of a lord, then she is referred to as Lady First Name. When she marries she may be referred to as Lady First Name (more familiar and used by friends) or as Lady Last Name. In Lady Katherine's Comeuppance, Lady Katherine was the daughter of an earl, so she was known as Lady Katherine from birth.
If a woman is not a daughter of a lord, but she marries a lord, then she is known as Lady Last Name. In Becoming Lady Amherst, Sarah is an American who marries Lord Jeffrey Amherst, therefore she is known as Lady Amherst, but not as Lady Sarah.
But, when Sarah and Jeffrey have children (and you know they will) then their daughters will be known as Lady First Name and their sons will be Lord First Name because their father is a lord.