Looking for that closed shop is a lost errand.
lost errand
idiomSynonym of fool's errand.
Searching for the missing keys in the dark park was a lost errand, so we gave up.
The detective realized that chasing the phantom lead through the city was a lost errand, yet he persisted against his better judgment.
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fool's errand
A foolish undertaking, especially one that is purposeless, fruitless, nonsensical, or certain to fail.
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get lost
To exit from the scene.
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look as if one had lost a shilling and found sixpence
To look very disappointed.
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look as if one has lost a shilling and found sixpence
To look annoyed or displeased.
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lost cause
A person or thing that is hopeless or futile.
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lost in the shuffle
Failing to stand out or receive attention as a result of a larger-scale change or transformation.
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lost in translation
Unable to be understood due to having been poorly translated.
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lost on
Not understood or appreciated by (someone).