  We measure the Cosmic Microwave Background (CMB) skewness power spectrum in
$\textit{Planck}$, using frequency maps of the HFI instrument and the
Sunyaev-Zel'dovich (SZ) component map. The two-to-one skewness power spectrum
measures the cross-correlation between CMB lensing and the thermal SZ effect.
We also directly measure the same cross-correlation using $\textit{Planck}$ CMB
lensing map and the SZ map and compare it to the cross-correlation derived from
the skewness power spectrum. We model fit the SZ power spectrum and CMB
lensing-SZ cross power spectrum via the skewness power spectrum to constrain
the gas pressure profile of dark matter halos. The gas pressure profile is
compared to existing measurements in the literature including a direct estimate
based on the stacking of SZ clusters in $\textit{Planck}$.
