Pesachim, chapter five, mishnah 2. A special law was established for the korban Pesach that does not apply to most offerings: in order for it to take on the status of a korban Pesach and be valid, its services must be performed lishmah - for the sake of the korban Pesach. It is not enough that the animal is designated as a korban Pesach; if it was slaughtered with the intention that it be a shelamim offering, which is a different type of offering, it is disqualified. An explicit intention that this is the korban Pesach is required.
The four services that require 'lishmah':
Shechitah - slaughtering the korban Pesach.
Kabbalas hadam - receiving the blood from the animal's neck after it is slaughtered, into a k'li shareis, one of the sanctified vessels of the Beis HaMikdash.
Holachah - carrying the blood from the place of slaughter to the altar.
Zerikah - throwing the blood onto the altar, at its designated place.
All four of these services must be performed lishmah, for the sake and purpose of the korban Pesach.
The words of the mishnah:
"Shechato shelo lishmo, v'kibel, v'hilech, v'zarak shelo lishmo" - he slaughtered the Pesach not for the sake of the korban Pesach but for the sake of a different offering, and likewise if he received the blood in a vessel, carried it toward the altar, or threw it onto the altar not for the sake of the korban Pesach.
And not only that, but even with a mixed intention:
"Lishmo v'shelo lishmo" - he performed one of the services first for the sake of the korban Pesach, and at the same time he also had in mind an intention that was not for the sake of the korban Pesach.
"Shelo lishmo v'lishmo" - he performed it first not for the sake of the korban Pesach, and afterward for the sake of the korban Pesach.
In all of these cases the offering is "pasul": it is not valid, he has not fulfilled his obligation of the mitzvah of the korban Pesach, and it must be burned in the place where all disqualified offerings are burned.
The mishnah explains how these two thoughts take shape:
"L'shem Pesach u'l'shem shelamim" - this is "lishmo v'shelo lishmo": he first had in mind that it is for the sake of the korban Pesach, and afterward for the sake of a shelamim offering, for although a shelamim resembles the korban Pesach, a shelamim is not a korban Pesach.
"L'shem shelamim u'l'shem Pesach" - this is "shelo lishmo v'lishmo": he first had in mind a shelamim offering, and afterward the korban Pesach.
In summary: the korban Pesach requires the intention of 'lishmah' in its four services - shechitah, kabbalah, holachah and zerikah. If one performed any one of them not for its own sake, or mixed into it an intention of lishmo and shelo lishmo in any order, the Pesach is disqualified, and he does not fulfill his obligation with it.