I am not sure I understand deeper reasons for your doubt, as even the examples from the Elem. Lewis that you are referring to seem on target, but the translation of usura as “interest paid for the use of money, usury” by L&S (usura, II, B) with a plethora of usage examples from the Classical era appears convincing enough to me.
Note also that two of the sources contrast sors and usura, respectively “principal” and “interest”:
debitor usuram pariter sortemque negabit (Mart. 5, 43, 3): the debtor will [not pay back] both interest and principal.
cures ut Atilio meo salva sit non sors modo verum etiam usura plurium annorum (full cit. Plin. Ep. 6.8.5) “make sure so that my dear Atillus would recover not only the principal but also [due/fair] interest for multiple years”
My understanding is that the English word interest has changed its meaning very significantly over the history of its use (Harper has to tell quite a story), and, as it took the modern unmarked meaning, the word “usury” began to be used in a marked, derogatory sense, standing in particular for “excessive, unjust interest.” But in Latin, usura was instead an apparently unmarked word for “interest.”
Also see a semantically related concept of faenus.
ADDED: If I am reading your concern that you find implausible the semantic shift of
"use" > (restriction) "use of lent money" > (metonymy) "payment for such use"
then, first of all, there is no doubt that usura the use and usura the interest is the very same lemma, no homonymy involved. If you look at the development of similar (legal, financial) concepts in English, the magnitude of change would be even greater. I already referred to the etymology of interest above; here's the breathtaking Story Of Fee, which can be abridged to:
"cattle" > "posession" > "real estate" > (merger with cognate) "fief, feudal estate" > "heritable estate" > "heritable privilege" > (metonymy) "payment to thus privileged" > "payment for privilege use" = (our current sense).
The stem of utor was very much active in Roman business and legal language (they reposessed property by usucapio and married per usum, and it was even one and the same thing from the standpoint of law, but I digress), so it is even less surprising for the stem to be productive in this domain.
I may be missing some fine point, but if I am, please consider expanding the question by clarifying why exactly would you find these pointers not satisfactory in your context.