new Vue({
     el: '#Application',
     router: Router,
     components: { 'ExampleDepartment', Application },
     data: function() {
          return {

          }
     }
});

<v-list-tile v-for="action in actions" :key="action.label" v-if="action.visibility == true">
     ...
</v-list-tile>

export default {
     watch: {
          $route: function() {
               this.getOrSetPageVisibility();
          }
     },

     methods: {
         getOrSetPageVisibility() {
               for(let index = 0; index < this.actions.length; index++) {
                    if(this.actions[index].page == this.$router.currentRoute.name) {
                         this.actions.$set(index, { visibility }, true);
                    }
               }
         }
     },

     data: function() {
          return {
               actions: [
                   {
                        label: 'Add Sample',
                        icon: 'add_circle',
                        page: 'Sample',
                        visibility: false
                   }
               ]
          }
     }
}