An L space with a d-separable square

In this note I will show that an inessential modification of the ZFC example of a hereditarily Lindelöf nonseparable space which was constructed in [J.T. Moore, A solution to the L space problem, J. Amer. Math. Soc. 19 (3) (2006) 717–736] has the property that its square contains a σ-discrete dense set.