  We determine non-perturbatively the parameters of the lattice HQET Lagrangian
and those of the time component of the heavy-light axial-vector current in the
quenched approximation. The HQET expansion includes terms of order 1/m. Our
results allow to compute, for example, the heavy-light spectrum and B-meson
decay constants in the static approximation and to order 1/m in HQET. The
determination of the parameters is separated into universal and non-universal
parts. The universal results can be used to determine the parameters for
various discretizations. The computation reported in this paper uses the
plaquette gauge action and the "HYP1/2" action for the b-quark described by
HQET. The parameters of the current also depend on the light-quark action, for
which we choose non-perturbatively O(a)-improved Wilson fermions.
