The answer for Lake County is yes, send a notorized original with a self addressed, stamped envelope and a check for $10 to the Clerks office.
A Florida "Declaration of Domicile" is a document which allows you to declare that you are a bona fide resident of Florida because you reside in and maintain a place of residence there. You intend to maintain the residence as your permanent home.
How to Become a Florida Resident, Officially