  We present the first lattice calculation of the B-meson binding energy
$\labar$ and of the kinetic energy $-\lambda_1/2 m_Q$ of the heavy-quark inside
the pseudoscalar B-meson. This calculation has required the non-perturbative
subtraction of the power divergences present in matrix elements of the
Lagrangian operator $\bar h D_4 h$ and of the kinetic energy operator $\bar h
\vec D^2 h$. The non-perturbative renormalisation of the relevant operators has
been implemented by imposing suitable renormalisation conditions on quark
matrix elements, in the Landau gauge. Our numerical results have been obtained
from several independent numerical simulations at $\beta=6.0$ and $6.2$, and
using, for the meson correlators, the results obtained by the APE group at the
same values of $\beta$. Our best estimate, obtained by combining results at
different values of $\beta$, is $\labar =190 \err{50}{30}$ MeV. For the
$\overline{MS}$ running mass, we obtain $\overline {m}_b(\overline {m}_b) =4.17
\pm 0.06$ GeV, in reasonable agreement with previous determinations. From a
subset of 36 configurations, we were only able to establish a loose upper bound
on the $b$-quark kinetic energy in a $B$-meson, $\lambda_1=\langle B \vert \bar
h \vec{D}^{2} h \vert B \rangle /(2 M_B )<$~1\, GeV$^2$. This shows that a much
larger statistical sample is needed to determine this important parameter.
