Hide/show customizer controls based on other settings in Customizer

you can define the conditional display on definition in PHP with somethign like that :

$wp_customize->add_control("course_instructor_layout", [
    // ... other arguments
    "settings" => "course_instructor_layout",
    "active_callback" => function ($control) {
        return !$control->manager->get_setting("lmscore_improved_summary")->value();
    },
]);

if that doesn’t work in your case, edit your question to add the complete definition of lmscore_improved_summary and course_instructor_layout.