Numerical simulations of neutron production from deuterium-lithium nuclear fusion reactions have been performed. A set of differential cross sections for the Li-7(d,xn) reaction for incident deuteron energies of up to 50MeV is assembled. The angular distribution of neutrons from a thick lithium target is simulated and benchmarked against experimental data. Two-stage neutron production from laser-target experiments has been studied as a function of laser intensity and energy. During the first stage a well collimated deuteron beam is generated using a high-intensity ultrashort pulse laser. During the second stage it is transported through a lithium target using a 3D Monte-Carlo ion beam-target deposition model. The neutron yield is estimated to be similar to 10(8) neutrons J(-1) laser energy. Some 10(10) neutrons can be expected from a similar to 100 J petawatt-class laser. For incident deuteron energies above 1 MeV the proposed scheme for neutron production from d-Li reactions is superior to that from d-d reactions, producing a collimated beam of neutrons with higher neutron yield.