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