In his Derashos El Ami, Rav Amiel notes an interesting distinction between the korban pesach and all other korbanos. With respect to a korban chatas, for example, which must be offered lishma, the halacha is that only shechting the chatas with the intent of offering it as different korban disqualifies it, but shechting it with the intent that it is chulin does not. With respect to the korban pesach, however, based on the words “zevach pesach hu la’Hashem” (see Rambam Hil Psulei haMukdashin ch. 15), the halacha is that even offering a korban pesach having in mind that it is chulin disqualifies the korban.
Both a chatas and the korban pesach must be offered “lishma”. Why is it that a chatas can be disqualified only by the lo lishma of having a different korban in mind, but the pesach is disqualified even by a lo lishma of having chulin in mind?
Rav Amiel explains (link) that after we already have achieved geulah, the thought of chulin while offering a korban does not diminish from the inherent sanctity of the offering. But while we are still erev pesach awaiting our geulah and preparing our korban pesach, while our redemption is still in its formative stages, the lack of lishma can corrupt, diminish, and pasul the entire enterprise.
I would add that perhaps this is why we celebrate the taking of the korban pesach on Shabbos and not on 10 Nissan. Shabbos is what defines the purpose of the rest of our workweek; it is the lishma of our existence.