The problem is that the language that you're using is the output language. For example if you try this
alert(moment("5 5 2014").lang("nl").format("DD/MMMM/YYYY"));
the output will be
05/mei/2014
In order to accept inputs in Dutch you will have to implement it. For example create a method which takes a string as a parameter and changes Dutch months to numbers, so when you call
moment(toMoment("5 mei 2014")).lang("nl").format("DD/MMMM/YYYY")
the return value of toMoment("5 mei 2014")
would be 5 5 2014
An example of that would be
function toMoment(str){
var result = null;
var splitted = str.split(" ");
var month = splitted[1];
switch(month){
case "mei": result = "5"; break;
}
return splitted[0] + " " + result + " " + splitted[2];
}