lost iphone

If you were using iCloud Messages, then logging in to iCloud on a new iPhone with the Apple ID from the old iPhone, and turning on the Messages option in iCloud settings would download those messages onto the iPhone.

See here: Keep all your messages in iCloud - Apple Support

Otherwise, if you had a backup from the old iPhone, it may contain those messages and can be restored onto a new iPhone to access them.

See here: Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

If neither of those is true, then there is no way to recover messages.

If you have a backup of the lost phone, you might be able to retrieve them by restoring the backup to another device.

Restoring from a backup erases all data currently on your device. Any data newer than when the backup was made will be erased. A restore is an all or nothing restore.

Backup - Restore your device from an iCloud or iTunes backup

You can also check your carrier's web site to see if you can access them there.