Mass and semi-major axis of the synthetic populations of planets around 0.2 M_⊙ stars, with our fiducial mass budget (Eq. (1) with β = 1; top) and a lower mass budget (Eq. (1) with β = 2; bottom). The colours represent icy embryos with initial and final positions outside the ice line (blue), mixed embryos that start outside and migrate to inside the ice line (purple), and rocky embryos with initial and final positions inside the ice line (red). The pebble isolation mass at the initial and final simulation time is marked by the dashed and solid grey line, respectively. The lensing sensitivity region, assuming the lens star is in the disc (4 kpc) and the source star is in the bulge (8 kpc), is marked with the dashed orange lines. The quadratic scaling of the accretion rate with stellar mass (bottom) hinders the formation of planets outside the ice line, as well as gas giants.