How do I convert a C# List<string[]> to a Javascript array?

You could directly inject the values into JavaScript:

//View.cshtml
<script type="text/javascript">
    var arrayOfArrays = JSON.parse('@Html.Raw(Model.Addresses)');
</script>

See JSON.parse, Html.Raw

Alternatively you can get the values via Ajax:

public ActionResult GetValues()
{
    // logic
    // Edit you don't need to serialize it just return the object

    return Json(new { Addresses: lAddressGeocodeModel });
}

<script type="text/javascript">
$(function() {
    $.ajax({
        type: 'POST',
        url: '@Url.Action("GetValues")',
        success: function(result) {
            // do something with result
        }
    });
});
</script>

See jQuery.ajax

Many way to Json Parse but i have found most effective way to

 @model  List<string[]>

     <script>

         function DataParse() {
             var model = '@Html.Raw(Json.Encode(Model))';
             var data = JSON.parse(model);  

            for (i = 0; i < data.length; i++) {
            ......
             }

     </script>

Many of these answers do work, but I have found the easiest way by far is to send data through ViewData or ViewBag and let JSON.Net serialize it.

I use this technique when Javascript is needed for HTML generation before the page load or when AJAX overhead needs to be avoided:

In the controller:

public ActionResult MyController()
{
    var addresses = myAddressesGetter();
    ViewData["addresses"] = addresses ;
    return View();
}

In the view:

@section scripts {
<script type="text/javascript">
    var MyjavascriptAddresses: @Html.Raw(JsonConvert.SerializeObject(ViewData["addresses"])),
</script>
}

You can always rely on JSON.NET whereas some browsers have poor JSON deserialization support. Another benefit over some methods in that you can see the Javascript using your browser's View --> Source, since it is simply text generated server-side.

Note that In most situations, Web API a more elegant way to get JSON to the client.