  In this paper, we study the large deviation principle (LDP) for obstacle
problems governed by a T-monotone operator and small multiplicative stochastic
reaction. Our approach relies on a combination of new sufficient condition to
prove LDP by Matoussi, Sabbagh and Zhang [\textit{Appl. Math. Optim.} 83:
849-879, 2021] and Lewy-Stampacchia inequalities to manage the
Lagrange-multiplier associated with the obstacle.
