Lady is used as the female equivalent of several different male titles, is part of some other female titles, along with being used as a "polite" term for woman (polite in "scare quotes" because it can be found objectionable in some circumstances, which would be an essay's worth of discussion in itself). It originally meant the mistress of a household; a sense which is mostly obsolete but not entirely extinct.
"My lady" can also be used as a form of address (though is mostly obsolete in non-ironic use).
As such there's a bewildering variety of ways in which a given person (especially if a man) addressing a given woman may or may not be using the term, depending on when in history it was, her social station, his relative social station, and his relationship to her.
And then there's a bunch more from ironic uses, or as pet names in some dialects (some dialects even have duchess as a way one might address one's wife, or perhaps even a woman generally).
"Lady wife" survives that confusing mess as a term half ironic and half straight, with tone perhaps leaning it heavily into the ironic ("oh oh! must not stay out drinking any later, the lady wife will not approve!") or more heavily into the straight ("my good lady wife is a joy and a rock of support to me").
About the closest you'd have for a woman to use of her husband is a very definitely ironic* use of "lord and master". Normally so ironic that it would more likely be used if she was speaking critical of him, than fondly.
*Barring some specialised tastes, so to speak.