Nilpotency of BRST operator in gravity

I am going through the BRST quantisation in Perturbative quantum gravity and looked at the papers of Nishijima and Ojima. I am confused about the closure of the BRST operator; I.e $s^2=0$, particularly in the case of the ghost field.

The BRST transform of the ghost field is:
$$sc^{mu} = c^{lambda}nabla_{lambda}c^{mu}$$

Therefore, $$s^2c^{mu}= sc^{lambda}nabla_{lambda}c^{mu}-c^{lambda}nabla_{lambda}sc^{mu}= c^{nu}nabla_{nu}c^{lambda}nabla_{lambda}c^{mu}-c^{lambda}nabla_{lambda}c^{nu}nabla_{nu}c^{mu}-c^{lambda}c^{nu}nabla_{lambda}nabla_{nu}c^{mu}=- c^{lambda}c^{nu}nabla_{lambda}nabla_{nu}c^{mu} $$

So I find $s^2 c^{mu}$ is not vanishing here. What mistake am I doing here?

Here is the link of the paper by Nishijima:
https://doi.org/10.1143/PTP.60.272

The particular equation numbers are: 2.25 and 2.26, in page number 275.