Yes, there is radiation in lightning. You can tell because lightning involves a bright flash of light, and every kind of light is radiation.

Scientists say that light is one type of electromagnetic radiation. It's pretty hard to explain exactly what the "electromagnetic" part of that sentence really means, but I just think of radiation as a more general category for light. Some other types of radiation are infrared light, ultraviolet light, microwaves, radio waves and X-rays. You can't see those types of radiation because human eyes are only made to see what we call visible light. But some animals can see infrared or ultraviolet light, and we can design machines that can detect different types of radiation.

Apart from being invisible to humans, any other properties of light that I can think of also apply to other types of radiation. For example, they travel in straight rays, and they move at the speed of light. When they hit a surface, they either pass through it, bounce off, or get absorbed and turned into heat (usually, they do some of each). All objects emit radiation, and objects that are hot emit more radiation.

When I imagine lightning, I think of yellow, blue or violet light. Lightning contains all these types of radiation. Lightning also probably contains invisible types of radiation like X-rays. I think these are hard to study: as far as I can tell, scientists still don't know everything about why lightning would generate the exact combination of radiation that it does.