Vue

HTML

<div id="app">
  <input v-on:blur="_close" v-on:keyup="_show"/>
  <ul v-if="open">
    <li v-on:click="set_data('A')">A</li>
    <li v-on:click="set_data('B')">B</li>
    <li v-on:click="set_data('C')">C</li>
  </ul>
  <div>
  {{letter}} 
  <!-- this letter will be always empty -->
  </div>
</div>

CSS

body {
  background: #20262E;
  padding: 20px;
  font-family: Helvetica;
}

#app {
  background: #fff;
  padding: 20px;
  transition: all 0.2s;
}

li {
  margin: 8px 0;
}

h2 {
  font-weight: bold;
  margin-bottom: 15px;
}

del {
  color: rgba(0, 0, 0, 0.3);
}
li{
  cursor: pointer;
}
li:hover{
  background: #ebebeb;
}

Vue

new Vue({
  el: "#app",
  data:{
  	open: false,
    letter: ""
    
  },
  methods: {
  	set_data(letter) {
    	this.letter = letter
    },
    _close(){
    	this.open = false;
      //i can add here setTimeOut function but i dont know how many  miliseconds/seconds blur will be pressed
      //someone can hold it for 10 - 20 just to proof that you cna not relay on setTimeout
    },
    _show(){
    	this.open = true;
    }
  }
})