I have been wondering about the question above for a while, as I’ve read quite a few novels lately that use the word “luncheon”, with seemingly no distinction between that word and “lunch”. I was too lazy to look it up, but, typing it in the search box, I found this short (1.5-minute) YouTube explanation below:
The Oxford English Dictionary agrees (the first meaning is “A large chunk of something, esp. bread, cheese, or some other food; a thick slice, a hunk; = lunch“). The relevant entry:
There you go. But I still would like to be able to invite a friend to a restaurant for an informal luncheon. That’s not correct, but it’s fun to say. And, at any rate, I don’t think I’ve heard anyone say “luncheon” lately, even referring to a formal meal. And in fiction it’s used incorrectly all the time.

Where I grew up, there was no such thing as lunch. It was breakfast, dinner and supper. 😄
I went down a rabbit hole looking at the history of meals and their names one time. Lots of variations compared to the modern norm. And a lot of it even comes down to families, i.e what you may think of as “where you grew up” is more about your own family’s household, while your nextdoor neighbor might have had a different usage (not always – some differences really were regional/temporal, but a lot were idiosyncratic). If you ever look up those dialect survey maps, the usage of “dinner” vs. “supper” ends up looking pretty random across the US.
I forgot how well links work in comments here, but here’s a link to one of those maps, if it comes through:
http://dialect.redlog.net/staticmaps/q_96.html
Generally probably so, but in rural northern Indiana in the 50s and 60s, nobody we knew used lunch and dinner for dinner and supper 😄
“…it’s used incorrectly all the time.”
As someone who favors descriptivism over prescriptivism, that’s a funny way of putting it. If a word is used a certain way all the time, then that now is the correct way. When dictionaries provide definitions, they’re merely listing the way a majority of speakers use a word, not acting as some authority that can prescribe the definition by fiat. Even etymology, while certainly interesting, doesn’t define modern usage.
+1. Thank you for the succinct expression.
As I see it, you can invite a friend to lunch or luncheon – the words here are interchangeable— but eating on your own is only lunch. “Formal” includes a verbal invitation.