If a lead were to create a conversation and they signed up, the conversations would be merged to the user account.

The conversations will then be forever tied to that user account. However, if they're chatting in from a lead account and happen to clear their cookies or use a different browser; a new lead will be created preventing you from seeing all of the conversations in the past.

You can ask them for their email so they have the option to open in messenger which will automatically sign them into that lead account.