<p>This paper is the second part of "A study on geodesics and lifespan of the Rindler-modified Schwarzschild black hole" [1] where we have investigated the time-like geodesics in the Rindler-modified Schwarzschild black hole (RMSBH) spacetime. In this part, we continue to study the null geodesics around the RMSBH. Based on this, we further explore the lifespan of the black hole. For the radial null geodesics, the relationship between the coordinate distance and the coordinate time is obtained. In addition, the expressions for the radius of the circular orbit formed by photons around the RMSBH and the impact parameter of the null geodesics are also derived. Meanwhile, we calculate the deflection angle of light rays grazing around the RMSBH and find that the cosmological constant does not affect the deflection angle of photons passing by the black hole, but the Rindler acceleration will reduce the deflection angle. In the thermodynamics part, our primary focus is on the radiation lifespan of the black hole. Our calculations reveal that both the Rindler acceleration and the cosmological constant can reduce the lifespan of the black hole.</p>