This is an example of a well-known and long-standing joke that is based on the changing the meaning of the original saying.
Firstly, the phrase, " ... dinner date at that new diner, Dinner" is almost a tongue-twister because of the repeated "d" and the difference in pronunciation between dinner and diner.
When someone says something that is difficult to pronounce, the other may reply, ironically, "That's easy for you to say!" The listener implies that (a) it wasn't easy to say (irony) and (b) that they themselves would be unable to say it correctly.
This can be said, whether the speaker said the phrase perfectly, or whether they stumbled over their words.
History of the humorous use of the phrase
I am old to enough to remember the British comedy duo, Eric Morecambe and Ernie Wise. They were hugely popular on British TV in the 1970's and 80's.
Eric Morecambe in particular had a number of catchphrases, For example, I quote (my emphasis):
Much of the material of the Morecambe and Wise shows consisted of
their well-worn catch phrases that recurred like motifs throughout
their career. Barely a show would go by without Eric referring to
Ernie's "short, fat, hairy legs",[6] or pointing out that "you can't
see the join", where Ernie's supposed wig was attached. Eric never
seemed to tire of offering his partner some "Tea, Ern?". This was a
pun on "tea urn", a vessel for serving hot drinks used in workplaces.
If anyone fluffed their line, Eric would usually say, "That's easy for you to say!" or "You can say that again".
https://en.wikipedia.org/wiki/Morecambe_and_Wise
Note that the idiom. "You can say that again", is also used in a non-standard and joking way by Eric Morecambe.
Whether this phrase predates the TV show, I can't say. However these comedians worked together as far back as the 1940's. Therefore I think it highly likely.