  Using grand-canonical Monte Carlo simulations, we investigate the phase
diagram of hard rods of length $L$ with additional contact (sticky) attractions
on square and cubic lattices. The phase diagram shows a competition between
gas-liquid and ordering transitions (which are of demixing type on the square
lattice for $L \ge 7$ and of nematic type on the cubic lattice for $L \ge 5$).
On the square lattice, increasing attractions initially lead to a stabilization
of the isotropic phase. On the cubic lattice, the nematic transition remains of
weak first order upon increasing the attractions. In the vicinity of the
gas-liquid transition, the coexistence gap of the nematic transition quickly
widens. These features are different from nematic transitions in the continuum.
