Here’s what I see:
This is the typical error that the free version of Live Links gives when the connection to the Local site is broken. This can be due to things like the Live Link expiring, the wifi connection for the computer being disrupted, or even if the computer has gone to sleep.
Because of this, sharing a Live Link is best done when the communication is happening in almost realtime. For something like sharing via email or here in the forums where a response might not be immediate, it might make more sense to deploy the site to a temporary location so that whoever you are sharing your work with can visit it on their own time.