We present TTCF4LAMMPS, a toolkit for performing non-equilibrium molecular dynamics (NEMD) simulations to study the fluid behaviour at low shear rates using the LAMMPS software. By combining direct NEMD simulations and the transient-time correlation function (TTCF) technique, we study the fluid response to shear rates spanning 15 orders of magnitude. We present two examples for simple monatomic systems: one consisting of a bulk liquid and another with a liquid layer confined between two solid walls. The small bulk system is suitable for testing on personal computers, while the larger confined system requires high-performance computing (HPC) resources. We demonstrate that the TTCF formalism can successfully detect the system response for arbitrarily weak external fields. We provide a brief mathematical explanation for this feature. Although we showcase the method for simple monatomic systems, TTCF can be readily extended to study more complex molecular fluids. Moreover, in addition to shear flows, the method can be extended to investigate elongational or mixed flows as well as thermal or electric fields. The high computational cost needed for the method is offset by the two following benefits: i) the cost is independent of the magnitude of the external field, and ii) the simulations can be made highly efficient on HPC architectures by exploiting the parallel design of the algorithm. We expect the toolkit to be useful for computational researchers striving to study the nonequilibrium behaviour of fluids under experimentally-accessible conditions.