<ion-item-sliding *ngFor="let list of list" >
         <ion-item>
           <p>An item:
             <strong>{{list.list1}}</strong>
           </p>
           <p>Oooooh is this important:
             <strong>{{list.list2}}</strong>
           </p>
            <p>Another item:
             <strong>{{list.list3}}</strong>
            </p>
       </ion-item>

         <ion-item-options side="left">
              <button ion-button color="danger" (click)="deleteList(list.id)">  // this should be id not key
                <ion-icon name="md-trash">Delete</ion-icon>
              </button>
         </ion-item-options>
       </ion-item-sliding>

import { EventProvider } from '../../providers/event/event';
import { User } from 'firebase/app'; // import user from firebase;
import * as firebase from 'firebase/app';

@IonicPage()

export class ListPage {
  /* public list: Array<any>; */
  lists = [];
  authenticatedUser: User; //declare variable authenticatedUser as type User
   constructor(
    public navCtrl: NavController,
    public eventProvider: EventProvider
  ) { firebase.auth().onAuthStateChanged(user => {
  if (user) {
    this.authenticatedUser = user;
}
 });
}

deleteList(key) {
firebase
   .database()
    .ref(`/userProfile/${this.authenticatedUser.uid}/List/${key}`).remove()
}

  ionViewDidLoad() {
    this.eventProvider.getlist().on('value', listSnapshot => {
      this.lists = [];
      listSnapshot.forEach(snap => {
        this.lists.push({
          id: snap.key,
          list1: snap.val()
        });
        return false; // why are you returning false dont use it.
      });
    });
  }

}