We report the results of the narrow-band photometry and imaging monitoring of comet C/2013 R1 (Lovejoy) with the robotic telescope TRAPPIST (La Silla observatory). We gathered around 400 images over 8 months pre- and post-perihelion between September 12, 2013 and July 6, 2014. We followed the evolution of the OH, NH, CN, C3, and C2 production rates computed with the Haser model, as well as the evolution of the dust production. All five gas species display an asymmetry about perihelion, since the rate of brightening is steeper than the rate of fading. The study of the coma morphology reveals gas and dust jets that indicate one or several active zone(s) on the nucleus. The dust, C2, and C3 morphologies present some similarities, while the CN morphology is different. OH and NH are enhanced in the tail direction. The study of the evolution of the comet activity shows that the OH, NH, and C2 production rate evolution with the heliocentric distance is correlated to the dust evolution. The CN and, to a lesser extent, the C3 do not display such a correlation with the dust. This evidence and the comparison with parent species production rates indicate that C2 and C3, on one hand, and OH and NH, on the other, could be – at least partially – released from organic – rich grains and icy grains. On the contrary, all evidences point to HCN being the main parent of CN in this comet.