According to [WikiPedia][1]:

>  The moulds are permitted a tolerance of up to two micrometres, to ensure the bricks remain connected.

But, as I noted in a comment, that is in an industrial environment, where great care is taken to ensure that not just a one-off piece is right, but that the entire batch of pieces is right. They probably take a [six sigma approach][3] or something similar.  
In a DIY setting, that is not necessary. A certain percentage of faulty pieces can be tolerated, as a home manufacturer probably has the time to check each piece and recycle the faulty ones.



![Main dimensions of Lego bricks (WikiPedia)][4]

The image above shows the main dimensions of Lego pieces. Based on its [source][6] and the measurements given in [this answer][5], we get 8.0mm per 20 LDU, or 0.4mm/LDU.

Since the smallest offset seen so far is [0.3 LDU][2], you would need at least a 0.12mm resolution to print _that brick_. But if you're printing pieces with a resolution of 1 LDU, you'd need a printer with at least a 1 LDU resolution.

So it depends on the resolution of the pieces you want to print.

[1]: http://en.wikipedia.org/wiki/Lego#Manufacture
[2]: https://bricks.stackexchange.com/a/2060/3176
[3]: http://en.wikipedia.org/wiki/Six_Sigma
[4]: https://upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Lego_dimensions.svg/1000px-Lego_dimensions.svg.png
[5]: https://bricks.stackexchange.com/a/692/3176
[6]: http://www.dimensionsinfo.com/dimensions-of-a-standard-lego-brick/