Yes, it will be your property (yours understood as you clientās).
Unlike many people who charge a monthly or annual license to use the page the landing page will be owned by you.
To develop the landing page I will use Joomla, Wordpress or pure Html (I generally prefer the first two solutions, Joomla in particular) and consequently you will not be tied to a licensing fee of a saas such as Instapage or Getresponse.
Please note: this does not mean you will not have annual costs: the cms must be kept up-to-date and secure, and the server has an annual cost. Consider a total expense of about 300ā¬ per year, all inclusive.