Mimic Vat and Exiling
Yes.  The relevant part of Mimic Vat's text reads:


  Put a token onto the battlefield that's a copy of the exiled card. It gains haste. Exile it at the beginning of the next end step.


The text clearly tells you to exile the token that the Vat created regardless of whether it's a creature or not.  If a Licid token becomes an enchantment, it is still the same object and thus still the same token, and so the Vat's delayed triggered ability will still find it and exile it at the next end step.