Map an array of arrays

const deepMap=(input,callback)=>input.map(entry=>entry.map?deepMap(entry,callback):callback(entry))

//test 

deepMap([1,2,3,[1,2]],x=>x*2) // [1,4,9,[1,4]]

You can make your code much cleaner with ES2015 arrow functions:

var array = [[1, 2], [3, 4]];
var double = x => x * 2;
var doubledArray = _.map( array, subarray => _.map( subarray, double ));

Using vanilla JS:

var array = [[1, 2], [3, 4]];
var double = x => x * 2;
var doubledArray = array.map( subarray => subarray.map( double ));

Just _.map it twice:

var array = [[1, 2], [3, 4]];
var doubledArray = _.map(array, function (nested) {
    return _.map(nested, function (element) {
        return element * 2;
    });
});

Or without lodash:

var doubledArray = array.map(function (nested) {
    return nested.map(function (element) {
        return element * 2;
    });
});

Furthermore, consider using es6 arrow functions:

var doubledArray = array.map(nested => nested.map(element => element * 2));

It's much more elegant to use the es6 destructuring syntax within your map statement:

array.map(([ a, b ]) => [ a*2, b*2 ]);