  We introduce the class of lattice-linear monomial ideals and use the
LCM-lattice to give an explicit construction for their minimal free resolution.
The class of lattice-linear ideals includes (among others) the class of
monomial ideals with linear free resolution and the class of Scarf monomial
ideals. Our main tool is a new construction by Tchernev that produces from a
map of posets $\eta:P\lra\mbb{N}^n$ a sequence of multigraded modules and maps.
