In this paper, we focus on the throughput of random access with power-domain non-orthogonal multiple access (NOMA) and derive bounds on the throughput. In particular, we demonstrate that the expression for the throughput derived in [1] is an upper-bound and derive a new lower-bound as a closed-form expression. This expression allows to find the traffic intensity that maximizes the lower-bound, which is shown to be the square root of the number of power levels in NOMA. Furthermore, with this expression, for a large number of power levels, we obtain the asymptotic maximum throughput that is increased at a rate of the square root of the number of power levels.