first problem is that "this" is not going to be the input, off the top of my head you can get that via $("input[name='letter_type']:selected"), or maybe :checked, but that's just jquery stuff.   
then, instead of having the params in the url, define the grid like:
$('#dg').datagrid({
	url: 'lists.php',
	queryParams: {
		ltype: 'default'
	}
});if you don't want a default then make lists.php return an empty set.  then you can use the 'load' method to change the queryParams and load the new data