Three-loop beta function and non-perturbative alpha(s) in asymmetric momentum scheme

We determine the three-loop coefficient of the beta function in the asymmet ric momentum subtraction scheme in Landau gauge. This scheme is convenient for lattice studies of alpha(s), the running coupling constant of QCD. We p resent high statistics lattice results for alpha(s) in the SU(3) Yang-Mills theory without quark, compare with the three-loop running and extract the value of the corresponding Lambda(<(MS)over bar>) parameter. We estimate th e systematic error coming from four-loop terms. We obtain the result: Lambd a(<(MS)over bar>) = 295 (5)(15)a(-1)(beta=6.0)/1.97GeV MeV.