This paper addresses the stabilization of aperiodic sampled-data Lure systems, where the nonlinearity is assumed to be both sector and slope restricted. Based on a looped-functional and a Lure-type function, this method provides sufficient stabilization conditions in the form of matrix inequalities. It is shown that the proposed conditions guarantee that the Lure-type function is strictly decreasing at the sampling instants, which also implies that the continuous-time trajectories converge asymptotically to the origin. As the derived matrix inequalities are LMIs provided some variables are fixed, we propose a Particle Swarm Optimization (PSO) algorithm to compute a nonlinear sampled-data state feedback control law aiming at maximizing the intersampling interval or the sector bounds for which the global asymptotic stability of the origin of the closed-loop system is guaranteed.