To make each of the columns autosize you can set Width="Auto" on the GridViewColumn.
To right-align the text in the ID column you can create a cell template using a TextBlock and set the TextAlignment. Then set the ListViewItem.HorizontalContentAlignment (using a style with a setter on the ListViewItem) to make the cell template fill the entire GridViewCell.
Maybe there is a simpler solution, but this should work.
Note: the solution requires both HorizontalContentAlignment=Stretch in Window.Resources and TextAlignment=Right in the CellTemplate.
<Window x:Class="WpfApplication6.Window1"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Title="Window1" Height="300" Width="300">
<Window.Resources>
<Style TargetType="ListViewItem">
<Setter Property="HorizontalContentAlignment" Value="Stretch" />
</Style>
</Window.Resources>
<Grid>
<ListView Name="lstCustomers" ItemsSource="{Binding Path=Collection}">
<ListView.View>
<GridView>
<GridViewColumn Header="ID" Width="40">
<GridViewColumn.CellTemplate>
<DataTemplate>
<TextBlock Text="{Binding Id}" TextAlignment="Right" />
</DataTemplate>
</GridViewColumn.CellTemplate>
</GridViewColumn>
<GridViewColumn Header="First Name" DisplayMemberBinding="{Binding FirstName}" Width="Auto" />
<GridViewColumn Header="Last Name" DisplayMemberBinding="{Binding LastName}" Width="Auto"/>
</GridView>
</ListView.View>
</ListView>
</Grid>
</Window>