If you want to access the dataContext then try this one.
XAML
<phone:LongListSelector Grid.Row="1"
Name="llsMsg"
LayoutMode="List"
VirtualizingStackPanel.VirtualizationMode="Recycling">
<phone:LongListSelector.ItemTemplate>
<DataTemplate>
<StackPanel>
<Grid>
<TextBlock Text="{Binding}"
Foreground="Black" />
<Button Content="View Details"
Width="200"
Click="Button_Click"/>
</Grid>
</StackPanel>
</DataTemplate>
</phone:LongListSelector.ItemTemplate>
</phone:LongListSelector>
C#
private void Button_Click(object sender, RoutedEventArgs e)
{
var dataContext = (sender as Button).DataContext;
var dataContext = (sender as Button).DataContext as YourDataModel;
}