Vuetify: 1.1.9
Vue: 2.5.17
Browsers: Chrome
OS: Windows 10
https://codepen.io/danielschmitz/pen/NBzMRb?&editors=101
From documentation example, we have:
<v-list-tile
v-for="item in items"
:key="item.title"
avatar
@click="onListTileItemClick()" <<<<<<<<<<<<<<<<<<<<<
>
<v-list-tile-avatar>
<v-icon :class="[item.iconClass]">{{ item.icon }}</v-icon>
</v-list-tile-avatar>
<v-list-tile-content>
<v-list-tile-title>{{ item.title }}</v-list-tile-title>
<v-list-tile-sub-title>{{ item.subtitle }}</v-list-tile-sub-title>
</v-list-tile-content>
<v-list-tile-action>
<v-btn icon ripple @click="onButtonInfoItemClick()"> <<<<<<<<<<<<<<<
<v-icon color="grey lighten-1">info</v-icon>
</v-btn>
</v-list-tile-action>
</v-list-tile>

Most helpful comment
@click.stop="...https://developer.mozilla.org/en-US/docs/Web/API/Event/stopPropagation