How can I shut down my lost iPhone?

You cannot power off the phone remotely, if that is what you are asking. The phone will power down though, when the battery runs down.

If you are trying to locate the phone on the Find My map, the phone does need to have a good battery charge, needs to be powered on, and needs a good Internet connection where it might be located.

You can erase the iphone remotely from Find My/iCloud account, and you can mark it as lost in this case the wallet will be disabled for example

Click here for information; in addition, post notices around where it got lost, and if applicable, contact the Lost & Found department of the facility involved.

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