Shouldn't 'leisurely'and 'nightly' both be tagged as adverbs too? "Leisurely we strolled to the lake" is a how I thought, and 'nightly'would be included as 'daily' and 'monthly' etc are. Is this so?
It depends on the context:
 Adjective: a leisurely walk
=> Here 'leisurely' modifies the noun 'walk'
 Adverb: Leisurely we strolled to the lake.
=> Here 'leisurely' modifies the verb 'strolled'.