  The standard-model extension (SME) is an effective field theory framework
aiming at parametrizing any violation to the Lorentz symmetry (LS) in all
sectors of physics. In this Letter, we report the first direct experimental
measurement of SME coefficients performed simultaneously within two sectors of
the SME framework using lunar laser ranging observations. We consider the pure
gravitational sector and the classical point-mass limit in the matter sector of
the minimal SME. We report no deviation from general relativity and put new
realistic stringent constraints on LS violations improving up to 3 orders of
magnitude previous estimations.
