This is one of those cases where it is helpful to understand your system and know your Conversion efficiency as well as your Mash Efficiency. In general, improving the crush will only improve Conversion and not Lauter Efficiency.
I saw improved efficiency by double crushing at my LHBC, but I was only getting ~75% Conversion Efficiency from their standard crush, leading to 60-65% Mash Efficiency. Now, with my own mill, I get 90%+ conversion, so there's little room for double crushing to further improve Mash Efficiency.
A decent rule of thumb, though, is that if you are seeing Mash Efficiencies in the 70's or less on a ~1.050 beer, then you are probably getting poor conversion and your Mash Efficiency has room to be improved by an improved crush (or other changes in procedure).