The Minchas Chinuch answers the question we started with yesterday – why a derasha of “lecha” is needed to disqualify a stolen sukkah when we already have a din of mitzvah haba’ah b’aveira – by distinguishing between two different types of disqualification. The halacha of mitzvah haba’ah b’aveira teaches that a person gets no credit for fulfilling his mitzvah obligation. With respect to the mitzvah of sukkah, this is not as bad as it sounds. Except for the first night of Sukkos, there is no obligation to eat in the sukkah. One can eat fruits, vegetables, meat, fish, etc. and never need a sukkah. It makes little difference if you don't get credit for fulfilling an obligation that does not exist in the first place.
However, the Torah adds an additional level of disqualification to the stolen sukkah. The pasuk of “lecha” teaches not only do you not get credit for fulfilling any obligation by sitting in a stolen sukkah, but more than that -- the sukkah itself is invalid. A stolen sukkah is like a sukkah without proper schach or walls. You don't have an obligation to eat in a sukkah on chol ha'moed, but if you do eat bread, it better be in a kosher sukkah.
As we discussed, there are Rishonim who explain that the added pasuk of "lecha" is needed because mitzvah haba’ah b’aveira applies only to mitzvos that involve “ritzuy,” supplication, such as korbanos. We ended off with the question (asked by the Ritva) of how these Rishonim explain the Yerushalmi that teaches that stolen matzah is a mitzvah haba’ah b’aveira -- matzah is not a mitzvah of ritzuy?!
Rav Betzalel Zolti (Mishnas Ya’avetz - link) answers by drawing a similar distinction to that of the Minchas Chinuch. There are two elements to the mitzvah haba’ah b’aveira disqualification: 1) a negation of credit for the mitzvah act, a psul in the ma’aseh gavra; 2) disqualification of the mitzvah object, a psul in the cheftza shel mitzvah. The Yerushalmi which disqualifies stolen matzah is speaking of disqualification of the mitzvah act -- one gets no credit for fulfilling the mitzvah of matzah by eating stolen food. This disqualification applies across the board to all mitzvos done through an aveira. The Rishonim that limit mitzvah haba’ah b’aveira to mitzvos of ritzuy are speaking only of the disqualification of the object, which is limited to specific cases.
The nafka minah between these views: what if a person ate in a stolen sukkah on Chol haMoed? If mitzvah haba’ah b’aveira only negates the credit one would have gotten for doing a mitzvah, since there is no mitzvah to eat in a sukkah on chol ha’moed anyway (e.g. one can avoid eating bread), there is no loss. However, if mitzvah haba’ah b’aveira disqualifies the object, eating in a stolen sukkah would be like eating in a sukkah without proper schach/walls, and would be prohibited.