Lenin also cites Engels in saying that production will still be organized:

State interference in social relations becomes, in one domain after another, superfluous, and then dies down of itself. The government of persons is replaced by the administration of things, and by the conduct of processes of production. The state is not ‘abolished’. It withers away. This gives the measure of the value of the phrase ‘a free people’s state’, both as to its justifiable use for a long time from an agitational point of view, and as to its ultimate scientific insufficiency; and also of the so-called anarchists’ demand that the state be abolished overnight.” (From Anti-Düring)

In short, only the violent / repressive elements of the state wither away, because their root cause, economic classes, wither away. IE, there’s no point in having proletarian armies and proletarian police, when the capitalist class they’re made to repress doesn’t exist anymore.

Here’s a good summary for the OP.