Manipulate retrieved ajax data in php

Yes you should use die(); in ajax function call, but because you’re not returning data and don’t care what is returned it’s not necessary

You should be using nonce, it’s good practice to get used to always using it regardless of the situation.

http://codex.wordpress.org/WordPress_Nonces
http://codex.wordpress.org/AJAX_in_Plugins

You should not be using a function called func, name it something specific to your setup, ie process_my_lat_lng

To solve the problem of the form being submitted twice, put the ajax call in a function and then call the function on page load:

jQuery(document).ready(function($){
    processMyLatLng();
});

function processMyLatLng() {
    var lat = 21.458965;
    var lng = -11.336985;
    jQuery.ajax( ajaxurl, {
        type: 'POST',
        data: {
            'action': 'func',
            'lat': lat,
            'lng': lng
        },
        success: function(data) {
            // note that i don't want the data to return back to the front-end.
        },
        error: function(errorThrown) {
            console.log(errorThrown);
        }
    });
}