Both korban chatas and korban pesach are listed in the mishna as exceptions to the standard rule. The standard rule is that if shechita is done shelo lishma the connection from the owner is broken, but it remains a kasher korban. Whereas chatas and pesach that are shechted shelo lishma are entirely invalid korbanos. Chatas and pesach are essentially the same in that their essence is to work for the owner, if the connection to the owner is broken, the korban becomes completely worthless. It would seem that there is no difference at all between chatas and pesach.
However, the gemara on 3a says that a chatas that is shechted l'sheim chulin (having in mind that it has no kedusha at all), doesn't impact the korban in any way. The rationale, as the gemara explains is - דמינה מחריב בה, דלאו מינה לא מחריב. This means that in order to be considered "shelo lishma" it must be something within the same general category as the korban, namely another korban, to the exclusion of chulin which is so out of left field it doesn't even qualify as shelo lishma. It should follow that a korban pesach that is shechted l'sheim chulin also has no impact on the korban for the same reason. BUT the Rambam (pesulei hamukdashin 15:11) writes that a korban pesach that is shechted l'sheim chulin becomes invalid. Why is korban pesach any different that chatas in this respect? Why don't we say by korban pesach as well that דמינה מחריב בה, דלאו מינה לא מחריב?
The Meshech Chochma (bo, 12:27) refers to his Ohr Sameiach where he elaborates on this issue. R. Meir Simcha explains that the whole concept of "l'sheim chulin" only applies to the act of slaughtering which applies to chulin, but doesn't have any place by the kabala and zerika which don't at all apply to chulin. That explains why chulin kavana during shechita could invalidate. Now, most korbanos have one function - to do the avoda of the blood to serve Hashem. Therefore, chulin which has an entirely different function - to eat the meat, has no commonality with kodshim in their essential purpose. That is the rationale behind דלאו מינה לא מחריב - l'sheim chulin doesn't ruin it since it is fundamentally so different. However, korban pesach if very different than other korbanos. Korban Pesach is primarily for the purpose of eating. That is why it is eaten b'tumah, and it must be shechted for eaters... Since korban pesach is fundamentally for the purpose of eating, it isn't so different than chulin in that respect. That is why intent for chulin will ruin a korban pesach. Although chulin is considered לאו מינה of most korbanos, it is considered מינה of chulin.