  The relationship between physical observables defined in lattice models and
the associated (quasi-)primary scaling operators of the underlying field-theory
is revisited. In the context of local scale-invariance, we argue that this
relationship is only defined up to a time-dependent amplitude and derive the
corresponding generalizations of predictions for two-time response and
correlation functions. Applications to non-equilibrium critical dynamics of
several systems, with a fully disordered initial state and vanishing initial
magnetization, including the Glauber-Ising model, the Frederikson-Andersen
model and the Ising spin glass are discussed. The critical contact process and
the parity-conserving non-equilibrium kinetic Ising model are also considered.
