  A density functional for the lattice gas (Ising model) from fundamental
measure theory is applied to the problem of droplet states in
three-dimensional, finite systems. Similar to previous simulation studies, the
sequence of droplets changing to cylinders and to planar slabs is found upon
increasing the average density $\bar\rho$ in the system. Owing to the
discreteness of the lattice, additional effects in the state curve for the
chemical potential $\mu(\bar\rho)$ are seen upon lowering the temperature away
from the critical temperature (oscillations in $\mu(\bar\rho)$ in the slab
portion and spiky undulations in $\mu(\bar\rho)$ in the cylinder portion as
well as an undulatory behavior of the radius of the surface of tension $R_s$ in
the droplet region). This behavior in the cylinder and droplet region is
related to washed-out layering transitions at the surface of liquid cylinders
and droplets. The analysis of the large-radius behavior of the surface tension
$\gamma(R_s)$ gave a dominant contribution $\propto 1/R_s^2$, although the
consistency of $\gamma(R_s)$ with the asymptotic behavior of the
radius-dependent Tolman length seems to suggest a weak logarithmic contribution
$\propto \ln R_s/R_s^2$ in $\gamma(R_s)$. The coefficient of this logarithmic
term is smaller than a universal value derived with field-theoretic methods.
