  There has been a proposal that infrared quantum effects of massless
interacting field theories in de-Sitter space may provide time-dependent
screening of the cosmological constant. As a concrete model of the proposal, we
study the three loop corrections to the energy-momentum tensor of massless
$\lambda \phi^4$ theory in the background of classical Liouville gravity in
$D=2$ dimensional de-Sitter space. We find that the cosmological constant is
screened in sharp contrast to the massless $\lambda \phi^4$ theory in $D=4$
dimensions due to the sign difference between the cosmological constant of the
Liouville gravity and that of the Einstein gravity. To argue for the robustness
of our prediction, we introduce the concept of time-dependent infrared
counter-terms and examine if they recover the de-Sitter invariance in the
$\lambda \phi^4$ theory in comparison with the Sine-Gordon model where it was
possible.
