If you want to style some menus independently read “Styling various menu differently from main” in the thread below
On the page you gave us, if you inspect the page with your browser developer tools, you will see that the vertical menu has the ID weaveriip_nav_menu-3
So you can remove the separating lines by adding the rule below in Advanced Options > Head section > Custom CSS Rule box
#weaveriip_nav_menu-3 .menu-vertical {border:none;}
#weaveriip_nav_menu-3 .menu-vertical li a {border:none;}
If you want to remove these on ALL the vertical menus use the rules below instead
.widget-area .menu-vertical {border:none;}
.widget-area .menu-vertical li a {border:none;}