Is there lactose in butter?

Not much. Some source say about 10% of the lactose content of whole milk. Some say just a trace. Either way many lactose intolerant persons may tolerate a little butter in their diet. You can experiment with your own degree of tolerance.
Very little . The butter-making process separates the majority of milk's water components from the fat components. Lactose, being a water soluble molecule, will largely be removed, but will still be present in small quantities in the butter unless it is also fermented to produce cultured butter. Clarified butter, however, contains very little lactose and is safe for most lactose intolerant patients.