That's no lady, that's my Mom.

The literal meaning, of course, is that he thinks that his mother is not a lady. However, I think that he was just being ironic, commenting on his mother's (overly) enthusiastic cheering to which the referee fell victim (her yelling was probably due to a (possibly) bad call made by the ref).

It's a reference to a bit of old vaudeville schtick: Q. Who was that lady I saw you with last night? A. That was no lady, that was my wife.

enoonIt's a reference to a bit of old vaudeville schtick: Q. Who was that lady I saw you with last night? A. That was no lady, that was my wife.

Yes, but I still think that a sentence like that one always carries a dose of irony. Don't you think so?

The remark was nothing more than a conscious reworking of the old gag. I would call it a contrived misinterpretation rather than irony.

I was thinking about the original sentence (as used in that old gag you mention). The comedian could have easily said "That was not just any lady, that was my wife". But he said "That was no lady, that was my wife", instead. I sure can see the irony there.

Yeah, I guess. I think we're just talking slightly at cross purposes, here. Irony is a tricky concept (Americans often don't get British irony, for one thing). I think of irony as more deliberate than what we have in this gag. The funny man is not supposed to be aware of the double meaning in what he's said. Henny Youngman's "Take my wife—please" is more like irony in my book.

I just want

enoonI just want to be sure that our friend Wowenglish knows what's going on with this locution

Well, I hope he won't see it as circumlocution, for one thing.