Logging in to the account from a different device wouldn't cause duplicate messages to appear on the phone itself, however it would explain your client's husband's immediate reaction to facebook posts.
The date/time issue you raise does sound like Lantern is reporting the message twice given the current date stamps. Have you contacted Lantern to see if this is perhaps a known glitch/issue with that version of iOS?
Do you have other tools to confirm findings (UFED, XRY)
As far as I'm aware for the spy tools to be installed on iPhones they need to be jailbroken and physical access to the phone is required to install the phone. If both these aren't met then the spy software scenario is unlikely IMO.
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