  Lorentz symmetry violations can be parametrized by an effective field theory
framework that contains both general relativity and the standard model of
particle physics called the standard-model extension (SME). We present new
constraints on pure gravity SME coefficients obtained by analyzing lunar laser
ranging (LLR) observations. We use a new numerical lunar ephemeris computed in
the SME framework and we perform a LLR data analysis using a set of 20721
normal points covering the period of August, 1969 to December, 2013. We
emphasize that linear combination of SME coefficients to which LLR data are
sensitive and not the same as those fitted in previous postfit residuals
analysis using LLR observations and based on theoretical grounds. We found no
evidence for Lorentz violation at the level of $10^{-8}$ for $\bar{s}^{TX}$,
$10^{-12}$ for $\bar{s}^{XY}$ and $\bar{s}^{XZ}$, $10^{-11}$ for
$\bar{s}^{XX}-\bar{s}^{YY}$ and
$\bar{s}^{XX}+\bar{s}^{YY}-2\bar{s}^{ZZ}-4.5\bar{s}^{YZ}$ and $10^{-9}$ for
$\bar{s}^{TY}+0.43\bar{s}^{TZ}$. We improve previous constraints on SME
coefficient by a factor up to 5 and 800 compared to postfit residuals analysis
of respectively binary pulsars and LLR observations.
