There are different ways of picking lights for animation, depending on which parameters you want to animate.

To animate a light's transformations (translation, rotation, scale) or visibility, pick the light in a modeling window or pick the appropriate light DAG node in the SBD window.

To animate any other light parameter, such as color, intensity, or glow, pick the light in the Multi-lister window. When animating a light through the Multi-lister, the light should not be active in the modeling window unless its transformations or visibility are also to be animated.

To copy all light animation from one light to another, select the root node of one light, and use Animation > Edit > Duplicate Animation Channels ❒ with Hierarchy set to BELOW and Parameters set to ALL in the Duplicate Channels Options box. The animation of individual light (or shader, or texture) parameters can be copied by selecting the source light in the Multi-lister, doing a -select of the light to be copied to in the Multi-lister, and then -selecting the desired parameters in the light (or shade, or texture) editor. Invoking Edit > Copy Parameters in the Multi-lister then copies the animation for that parameter.