You can create a new Page and simply put your LongListSelector in it.
For example (Page is called MyPopupPage
):
<Grid x:Name="ContentPanel" Grid.Row="1" Margin="12,0,12,0">
<con:LongListSelector x:Name="LongListSelector">
<con:LongListSelector.ItemTemplate>
<DataTemplate>
<TextBlock Text="{Binding Name}"/>
</DataTemplate>
</con:LongListSelector.ItemTemplate>
</con:LongListSelector>
</Grid>
Then fill it with whatever you want (Refer to: http://msdn.microsoft.com/en-us/library/windowsphone/develop/jj244365(v=vs.105).aspx)
In your MainPage (the page which should open the popup): Create an object of type Popup like:
Popup LLSPopup = new Popup();
And create a Method to set the MyPopupPage as the overlay of the popup:
private void ShowPopup()
{
MyPopupPage ovr = new MyPopupPage();
this.LLSPopup.Child = ovr;
this.LLSPopup.IsOpen = true;
}