An image stabilization control apparatus includes at least one processor or circuit which functions as an obtaining unit configured to obtain resolving power of an imaging system, a control unit configured to control a correction unit configured to correct an effect of shake acting on an imaging apparatus to which the lens apparatus is attached on the captured image, and a setting unit configured to set responsiveness of the correction unit controlled by the control unit based on the resolving power of the imaging system and an imaging condition, wherein the setting unit is configured to, in a case where the imaging condition satisfies a predetermined condition and the resolving power of the imaging system has a first value, set the responsiveness of the correction unit to be higher than in a case where the resolving power has a second value less than the first value.