In modern American usage, only the first would be correct in the sense of meeting a friend for a quick, casual midday meal. "Luncheon" refers to a more formal, organized entertainment.
When Bob retires next month, management will host a luncheon in his honor.
"Let's have lunch [not "a lunch"] at the diner" is roughly the equivalent of "Let's meet for lunch at the diner."
(not a teacher)
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