Tyzick is definitely English as you can see at
http://www.familysearch.org/Eng/Search/frameset_search.asp. It must be a variant of Tyzack which according to my sources comes from one of the places named Tizac is southwestern France which you can situate more precisely at
http://www.ign.fr/rubrique.asp?rbr_id=865&saisie=22119. I don't know the origin of Lyzack and Lizick but there's no evidence that they're Slavic in origin.