The next mitzvah in the past

Regarding the verse "Speak to the children of Israel and say to them, 'When a man from among you offers an offering…" (Leviticus 1:2) it is quoted in the Midrash (Leviticus Rabbah): "Rabbi Barachiah said to him, 'The Holy One, blessed be He, said to this man, Adam, your offering shall be like the offering of the first man, who had all his inheritance and did not offer anything from plunder or from the fivefold, even so you shall not offer anything from plunder or from the fivefold, and if you do so, it will be well. "To the Lord belong the words of a prophet."

And apparently an explanation is needed: after all, there is a well-known rule in the entire Torah that "a mitzvah that comes with a transgression is not a mitzvah" (Rambam, Sukkah, 3:1). And if so, what is the reason that with regard to sacrificing a sacrifice, there would be a difference in this?

And it should not be said that the law of "a mitzvah that comes with an offense" is learned from this verse itself, since in Tractate Sukkah (30a), the prohibition of using a stolen lulav is learned from another verse:

"…Gezul Shlomo is the first day of the Tov, which is written for you by your own law, but on the second day of the Tov, not by Rabbi Yochanan, because of Rabbi Shimon ben Yochi, because of God, it is a mitzvah that comes in transgression, as it is said, and you bring gezul, and the Passover, and the sick, gezul, like that of Passover, from which Pesach is made lawful, even gezul, for which is made lawful."
In other words: What is it about the lulav that requires a special verse or why didn't we just settle for the lulav?