You can set your attached property in ItemContainerStyle
:
<ListBox ItemsSource="{Binding itemList}" x:Name="list">
<ListBox.ItemTemplate>
</ListBox.ItemTemplate>
<ListBox.ItemContainerStyle>
<Style TargetType="ListBoxItem">
<Setter Property="AutomationProperties.AutomationId" Value="{Binding MyAutomationIdProperty}"/>
</Style>
</ListBox.ItemContainerStyle>
</ListBox>