I don't think there'd be anything "wrong" with using adverbially here, so it's hard to answer "why" without knowing the author's intent.
> Lively* opinions were exchanged.
>
> Opinions were exchanged in a lively manner.
Either way, the difference boils down to a slight nuance if you read the sentences literally. The "issue" here is that the translation you provided smoothed over the difference to be more readable in English (which isn't actually a problem) at the cost of being a less literal rendering of the Japanese.
*"" in this case is likely a use of hypallage as an opinion can't actually be in and of itself "lively," which explains in part the translator's motivation for affixing the idea of liveliness to the exchange of the ideas.