Ice accretion is an important problem and passive approaches for reducing ice-adhesion are of great interest in various systems such as aircrafts, power lines, wind turbines, and oil platforms. Here, we study the ice-adhesion properties of lubricant-impregnated textured surfaces. Force measurements show ice adhesion strength on textured surfaces impregnated with thermodynamically stable lubricant films to be higher than that on surfaces with excess lubricant. Systematic ice-adhesion measurements indicate that the ice-adhesion strength is dependent on texture and decreases with increasing texture density. Direct cryogenic SEM imaging of the fractured ice surface and the interface between ice and lubricant-impregnated textured surface reveal stress concentrators and crack initiation sites that can increase with texture density and result in lowering adhesion strength. Thus, lubricant-impregnated surfaces have to be optimized to outperform state-of-the-art icephobic treatments.