Analysis of the gauge residual freedom in the relativistic theory of lunar motion demonstrates that lunar laser ranging (LLR) is not currently capable to detect gravitomagnetic effects.
@article{arxiv.gr-qc/0702120,
title = {Comment on "The gravitomagnetic influence on gyroscopes and on the lunar orbit"},
author = {Sergei M. Kopeikin},
journal= {arXiv preprint arXiv:gr-qc/0702120},
year = {2008}
}