You can simply chain _.omit() with _.isUndefined and _.isNull compositions, and get the result with lazy evaluation.

Demo

var result = _(my_object).omit(_.isUndefined).omit(_.isNull).value();

Update March 14, 2016:

As mentioned by dylants in the comment section, you should use the _.omitBy() function since it uses a predicate instead of a property. You should use this for lodash version 4.0.0 and above.

DEMO

var result = _(my_object).omitBy(_.isUndefined).omitBy(_.isNull).value();

Update June 1, 2016:

As commented by Max Truxa, lodash already provided an alternative _.isNil, which checks for both null and undefined:

var result = _.omitBy(my_object, _.isNil);

If you want to remove all falsey values then the most compact way is:

For Lodash 4.x and later:

_.pickBy({ a: null, b: 1, c: undefined }, _.identity);
>> Object {b: 1}

For legacy Lodash 3.x:

_.pick(obj, _.identity);

_.pick({ a: null, b: 1, c: undefined }, _.identity);
>> Object {b: 1}

The correct answer is:

_.omitBy({ a: null, b: 1, c: undefined, d: false }, _.isNil)

That results in:

{b: 1, d: false}

The alternative given here by other people:

_.pickBy({ a: null, b: 1, c: undefined, d: false }, _.identity);

Will remove also false values which is not desired here.