Sorry for the answer which should have been a comment, but I do not have enough points for a comment.
I think that from a usage point of view, the second sentence sounds better with "de". The answer to this is probably to be found in the numerous words which do not appear in the sentence, and are just omitted to avoid repetition and complication. There is probably a verb, or even a clause, which should be there before the "de" but has been omitted for style.
ADDENDUM
Looking at the question again, I can see that the two sentences posting by the OP are not quite grammatically identical:
In the first one, "mentir" and "dire" are clearly equally complementing "choisit", itself demanding "de". The sentence will not work well with "plutôt que dire...".
In the second sentence, the first clause (which is inverted and through me at first) not only does not have an infinitive, which breaks the symmetry, but also has the verb "préfère" which somehow gives the choice of adding "de" or not.
I am wondering if, originally, there was a special rule/usage of "plutôt que" which allowed to be followed by "de" or not, depending on the verb of the first clause and whether the choice revealed by "plutôt" contained infinitives or not. Can anyone versed in old French answer this?