  Lattice results, kinematical constraints and QCD dispersion relations are
combined for the first time to derive model-independent bounds for QCD form
factors and corresponding rates. To take into account the error bars on the
lattice results we develop a general formalism which ascribes well-defined
statistical properties to these bounds. We concentrate on $\bar B^0 \to \pi^+
l^- \bar\nu_l$ decays because of the relative simplicity of the analytical
behavior of the relevant polarization functions and because of their immediate
phenomenological relevance. To determine the range of applicability of the
dispersive matching required to obtain the bounds, we have evaluated the
leading perturbative and non-perturbative QCD corrections to the relevant
polarization functions. Despite the lattice results' large error bars and
limited kinematical range, the bounds we obtain appear to favor certain
parametrizations for the form factors over others. The bounds also enable the
determination of $|V_{ub}|$ from the total experimental rate with a theoretical
error ranging from 27% to 37%, depending on the assumptions made. The
techniques developed here are, in fact, quite general and are not limited to
use with lattice results nor to semileptonic $\bar B^0 \to \pi^+ l^- \bar\nu_l$
decays.
