An assessment of the coolant reactivity feedback influence on a small Lead-cooled Fast Reactor (LFR) dynamics has been made aimed at providing both qualitative and quantitative insights into the system transient behavior depending on the sign of the above mentioned coefficient. The need of such an investigation has been recognized since fast reactors cooled by heavy liquid metals show to be characterized by a strong coupling between primary and secondary systems. In particular, the coolant density and radial expansion coefficients have been attested to play a major role in determining the core response to any perturbed condition on the Steam Generator (SG) side. The European Lead-cooled SYstem (ELSY)-based demonstrator (DEMO) has been assumed as the reference LFR case study. As a first step, a zero-dimensional dynamics model has been developed and implemented in MATLAB/SIMULINK® environment; then typical transient scenarios have been simulated by incorporating the actual negative lead density reactivity coefficient and its opposite. In all the examined cases results have shown that the reactor behaves in a completely different way when considering a positive coolant feedback instead of the reference one, the system free dynamics resulting moreover considerably slower due to the core and SG mutually conflicting reactions. The outcomes of the present analysis may represent a useful feedback for both the core and the control system designers.