Vue update variable not working

I’m replacing the value with lang() but the page doesn’t change until refreshed

App.vue
    data()
    {
           return {
                  message: {
                         tr: {
                                 'Mobil_Menu' : 'Mobil Menü',
                                 'Sifre': 'Şifre'
                          },
                          en: {
                                 'Mobil_Menu' : 'Mobile Menü',
                                 'Sifre': 'Password'
                         },
                 },
                currentLocaleid:'tr',
                currentLocalename:'Türkçe',
                currentLocaleflag:'turkey.png',
               locales: [ {id: 'tr', name: 'Türkçe', flag: 'turkey.png'}, {id: 'en', name: 'English', flag: 'united-kingdom.png'}]
          }
     },
        methods:
        {
           lang(e,f){
                    this.currentLocaleid = e;
                    this.currentLocaleflag = f
                 }
          }
    };

Other Page:
    data() 
    {
           return {
               message: this.$parent.message,
               currentLocaleid: this.$parent.currentLocaleid,
           }
    }

Other Page HTML:
<label>{{ message[currentLocaleid].Password}}</label>

How are you triggering the lang(), is there click event or something i am missing?