How do I build JSON dynamically in javascript?

As myJSON is an object you can just set its properties, for example:

myJSON.list1 = ["1","2"];

If you dont know the name of the properties, you have to use the array access syntax:

myJSON['list'+listnum] = ["1","2"];

If you want to add an element to one of the properties, you can do;

myJSON.list1.push("3");

First, I think you're calling it the wrong thing. "JSON" stands for "JavaScript Object Notation" - it's just a specification for representing some data in a string that explicitly mimics JavaScript object (and array, string, number and boolean) literals. You're trying to build up a JavaScript object dynamically - so the word you're looking for is "object".

With that pedantry out of the way, I think that you're asking how to set object and array properties.

// make an empty object
var myObject = {};

// set the "list1" property to an array of strings
myObject.list1 = ['1', '2'];

// you can also access properties by string
myObject['list2'] = [];
// accessing arrays is the same, but the keys are numbers
myObject.list2[0] = 'a';
myObject['list2'][1] = 'b';

myObject.list3 = [];
// instead of placing properties at specific indices, you
// can push them on to the end
myObject.list3.push({});
// or unshift them on to the beginning
myObject.list3.unshift({});
myObject.list3[0]['key1'] = 'value1';
myObject.list3[1]['key2'] = 'value2';

myObject.not_a_list = '11';

That code will build up the object that you specified in your question (except that I call it myObject instead of myJSON). For more information on accessing properties, I recommend the Mozilla JavaScript Guide and the book JavaScript: The Good Parts.