Here's Lucy (1968)

S2E11 Lucy and Johnny Carson

Lucy makes an appearance on the Johnny Carson show, where she participates in "stump the band" and ends up winning a dinner at the Brown Derby. As luck would have it, both Lucy and Uncle Harry choose the same night to dine there as Johnny Carson and Ed McMahon. Convincing herself that she’s won a dinner with the two stars, Lucy eagerly joins their table, leading to a series of amusing misunderstandings.