Can a Pokémon be both Shiny and Lucky?

Solution 1:

this is my first post on here (hopefully I’ve done it right!) I was lucky to end up with a 100% lucky shiny Eevee following a trade, so it is possible, but up to RNG.

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Solution 2:

Yes, it is possible.

Evidenced by another user in my town's Discord group, screenshot used with permission.

Shiny and Lucky Eevee