Estoy tratando de usar los siguientes datos JSON para crear la siguiente estructura similar en una función interna recursiva sin mucha suerte, realmente necesito ayuda y, si alguien puede ayudar, por favor. Gracias de antemano

<ul>
    <li></li>
    <li>
        <a href=""></a>
        <div>
            <ul>
                <li>
                    <a href=""></a>
                    <div>
                         ....etc
                    </div>
                </li>
            </ul>
        </div>
    </li>
</ul>

los datos JSON que estoy usando son los siguientes:

    var JSON = {
    menu: [
        {id: '0',sub: [
            {name: 'lorem ipsum 0-0',link: '0-0', sub: null},
            {name: 'lorem ipsum 0-1',link: '0-1', sub: null},
            {name: 'lorem ipsum 0-2',link: '0-2', sub: null}
            ]
        },
        {id: '1',sub: null},
        {id: '2',sub: [
            {name: 'lorem ipsum 2-0',link: '2-0', sub: null},
            {name: 'lorem ipsum 2-1',link: '2-1', sub: null},
            {name: 'lorem ipsum 2-2',link: '2-2', sub: [
                {name: 'lorem ipsum 2-2-0',link: '2-2-0', sub: null},
                {name: 'lorem ipsum 2-2-1',link: '2-2-1', sub: null},
                {name: 'lorem ipsum 2-2-2',link: '2-2-2', sub: null},
                {name: 'lorem ipsum 2-2-3',link: '2-2-3', sub: null},
                {name: 'lorem ipsum 2-2-4',link: '2-2-4', sub: null},
                {name: 'lorem ipsum 2-2-5',link: '2-2-5', sub: null},
                {name: 'lorem ipsum 2-2-6',link: '2-2-6', sub: null}
            ]},
            {name: 'lorem ipsum 2-3',link: '2-3', sub: null},
            {name: 'lorem ipsum 2-4',link: '2-4', sub: null},
            {name: 'lorem ipsum 2-5',link: '2-5', sub: null}
            ]
        },
        {id: '3',sub: null}
    ]
}

y el código que he creado (incompleto, este es el acertijo en el que necesito ayuda) es:

$(function(){

    $.fn.dropdown = function(settings){
        var that = this;
        var settings = $.extend({}, $.fn.dropdown.defaults, settings);
        var methods = {
            isArray: function(o){
                return Object.prototype.toString.call(o) === '[object Array]';
            },
            createDropdownCode: function(arr){
                var menu = arr.menu;
                var html = null;
                var menusort = function(menu){
                    html = that;

                    that.find("li").each(function(idx){

                        var menuList = menu[idx].sub;
                        var baseContainer = $(this);
                        var count = -1;

                        var subsort = (function(){

                            count += 1;

                            return function(submenu, pb){

                                var subblock;
                                subblock = $("<div />").append('<ul />');

                                if(methods.isArray(submenu)){

                                    for(var i=0;i<submenu.length;i++){

                                        var l = $("<li />").append("<a href='"+ submenu[i].link +"'>"+ submenu[i].name +"</a>");

                                        subblock.find('ul').app,end(l);

                                        if(pb !== undefined && i == submenu.length-1){
                                            pb.append(subblock)
                                        }

                                        if(methods.isArray(submenu[i].sub)){
                                            subsort(submenu[i].sub, subblock.find('ul li').eq(i));
                                        }

                                    }
                                }
                            }
                        })()
                        subsort(menuList)
                    })
                }
                menusort(menu);
                return null; //html !== null ? html.html() : null;
            },
            init: function(){

                // filter through json
                // create the div=>ul=>li
                if(settings.jsonData === undefined || settings.jsonData === null){
                    console.warn('No JSON Data passed')
                    return;
                }else{
                    if(!methods.isArray(settings.jsonData.menu)){
                        console.warn('No JSON Data passed')
                        return; // error, no data!
                    }
                }


                //var html = methods.createBlock(settings.jsonData.menu[0].sub);
                var html = methods.createDropdownCode(settings.jsonData);
                //console.log(html) 
            }
        }

        methods.init();

        return that;

    }

    $.fn.dropdown.defaults = {
        jsonData: null
    }

})

$('#menu').dropdown({
    jsonData: JSON
});

e utilizó el código integrado, gracias a la persona que dio una respuesta lo suficientemente cercana, aunque estudiará a los demá

$.fn.dropdown = function(settings){

    var that = this;
    var settings = $.extend({}, $.fn.dropdown.defaults, settings);

    var methods = {
        createDropDownCode: function(arr){

            // loop through li's of primary menu
            that.find("li").each(function(idx){

                $(this).append( menusort(arr.menu[idx].sub) );

                function menusort(data){
                    if(data !== null)   
                        var html = "<div><ul>";

                    for(item in data){
                        html += "<li>";
                        if(typeof(data[item].sub) === 'object'){
                            html += "<a href='" + data[item].link + "'>" + data[item].name + "</a>";
                            if($.isArray(data[item].sub))
                                html += menusort(data[item].sub);
                        }
                        html += "</li>"
                    }
                    if(data !== null)
                        html += "</ul></div>";
                    return html;
                }
            })
        },
        init: function(){
            var html = methods.createDropDownCode(settings.jsonData);

        }
    }

    methods.init();

}