  In this paper we present the tools to optimally extract the
Lensing-Integrated Sachs Wolfe (L-ISW) bispectrum signal from future CMB data.
We implement two different methods to simulate the non-Gaussian CMB maps with
the L-ISW signal: a non-perturbative method based on the FLINTS lensing code
and the separable mode expansion method. We implement the Komatsu, Spergel and
Wandelt (KSW) optimal estimator analysis for the Lensing-ISW bispectrum and we
test it on the non-Gaussian simulations in the case of a realistic CMB
experimental settings with an inhomogeneous sky coverage. We show that the
estimator approaches the Cramer-Rao bound and that Wiener filtering the L-ISW
simulations gives a slight improvement on the estimate of $f_{NL}^{L-ISW}$ of
$\leq 10%$. For a realistic CMB experimental setting accounting for anisotropic
noise and masked sky, we show that the linear term of the estimator is highly
correlated to the cubic term and it is necessary to recover the signal and the
optimal error bars. We also show that the L-ISW bispectrum, if not correctly
accounted for, yields an underestimation of the $f_{NL}^{local}$ error bars of
$\simeq 4%$. A joint analysis of the non-Gaussian shapes and/or L-ISW template
subtraction is needed in order to recover unbiased results of the primordial
non-Gaussian signal from ongoing and future CMB experiments.
