I see what you mean; it does look confusing.
The explanation is that lively is an adjective but widely is an adverb.
To make comparatives of short adjectives (one syllable), as I’m sure you know, you add –er. Adjectives of two syllables that end in –y follow the same rule, for example, easier. For most other adjectives of two syllables, you use “more” to form the comparative, eg more polite.
However, with adverbs of two syllables that end in –ly, you use “more”. Other examples include more quickly (not quicklier) and more clearly (not clearlier).
I hope this clarifies things for you.