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For $2\le p<\infty$ we show the lower estimates \[ \|A^{\frac 12}x\|_p \kl c(p)\max\{\pl \|\Gamma(x,x)^{{1/2}}\|_p,\pl \|\Gamma(x^*,x^*)^{{1/2}}\|_p\} \] for the Riesz transform associated to a semigroup $(T_t)$ of completely positive maps on a von Neumann algebra with negative generator $T_t=e^{-tA}$, and gradient form \[ 2\Gamma(x,y)\lel Ax^*y+x^*Ay-A(x^*y)\pl .\] As additional hypothesis we assume that $\Gamma^2\gl 0$ and the existence of a Markov dilation for $(T_t)$.
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