According to WikiPedia:
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 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.
The image above shows the main dimensions of Lego pieces. Based on its source and the measurements given in this answer, we get 8.0mm per 20 LDU, or 0.4mm/LDU.
Since the smallest offset seen so far is 0.3 LDU, 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.
