touch events firing twice

Your issue is that your function is getting triggered twice (once for each event type). See the DEMO here (I used mousedown and click as I am on a desktop right now - but its the same principle).

You need to catch and handle duplicate calls to the event. You could try setting a handled boolean so the click event knows if the touch event handled the event or not (the touch event should be firing first). Something like this...

var handled = false;
$(document).on("touchend click", ".lines-button", function(e){
    e.stopImmediatePropagation();

    if(e.type == "touchend") {
        handled = true;
        handleIt();
    }
    else if(e.type == "click" && !handled) {
        handleIt();
    }
    else {
        handled = false;
    }
});

function handleIt() { 
        if($(this).hasClass("close")){
            $(this).removeClass("close");
            $(".widget1x1Back").next(".actionsHolder3").slideUp("fast", function() {
                $(this).remove();
            });             
        }else{

            var iconsList = $(this).closest(".top1x1").next(".hdnActnLst").find(".iconsHolder3").html();
            $(this).closest(".widget1x1").append(iconsList);
            $(this).closest(".widget1x1").find(".actionsHolder3").hide();
            $(this).closest(".widget1x1").find(".actionsHolder3").slideDown(700,"easeOutBack");
            $(this).addClass("close");  
        } 
}

In most cases the following code will be ok:

$(document).on("touchend click", ".lines-button", function(e){
    if(e.type == 'touchend'){
        $(this).off('click');
    }
});

If touchend works, you may get rid of click.