M'lady is how a servant, in older British English, addresses a woman of a noble family. It is only my lady said quickly, with the y squeezed out. You meet it in historical films and manor-house stories — a footman at the door: This way, m'lady. Nobody in a modern shop should say it, and Taiwan students do not need it for real life. Though actually, younger people on the internet sometimes say m'lady as a joke, copying an over-polite man in a hat who bows too much. That joke is teasing, not respectful. The old use is formal and class-marked; the meme use is comic. Both are my lady in disguise.