Metal-halide perovskites are promising lasing materials for realization of monolithically integrated laser sources, the key components of silicon photonic integrated circuits (PICs). Perovskites can be deposited from solution and require only low temperature processing leading to significant cost reduction and enabling new PIC architectures compared to state-of-the-art lasers realized through costly and inefficient hybrid integration of III-V semiconductors. Until now however, due to the chemical sensitivity of perovskites, no microfabrication process based on optical lithography and therefore on existing semiconductor manufacturing infrastructure has been established. Here, the first methylammonium lead iodide perovskite micro-disc lasers monolithically integrated into silicon nitride PICs by such a top-down process is presented. The lasers show a record low lasing threshold of 4.7 ${mu}$Jcm$^{-2}$ at room temperature for monolithically integrated lasers, which are CMOS compatible and can be integrated in the back-end-of-line (BEOL) processes.