Well, if youi're planning on changing the functionality and design of your new list page (I'm assuming you are), the cleanest way to accomplish this is to actually create four new files:
(of course, you can change "newlist" to whatever name you want)
The tpl file contains the layout and HTML for your page, the LC_Page file contains the actual functionality and logic behind the page in PHP and the newlist.php file is what essentially calls all of the others.
Now, each of those files should contain the code of their "list page" counter parts. So, for example, LC_Page_Products_Newlist.php should contain the contents of LC_Page_Products_List.php and newlist.tpl should contain the contents of list.tpl, etc.
You'll also want to call your .tpl file from the LC file. So, in the action function you can add $this->tpl_mainpage = "products/newlist.tpl"
I hope that helps. This is how I usually do it, but maybe there's an easier way. EC Cube staff might have a better solution. Good luck!