One of the unusual laws regarding the korban pesach is that it can only be eaten leminuyav, by those who were specifically intended to be included as part of that particular sacrifice at the time of the slaughtering of the animal. With the animal being slaughtered on the 14th of Nissan and eaten only later that evening on the 15th, the question arose as to the status of those who were ritually impure—and thus, unable to partake of sacrificial meat—on the 14th of Nissan when the korban was slaughtered, but who would become ritually pure on the 15th, when the korban pesach was actually eaten.
Whereas by other korbanot, it is the bringing of the sacrifice that is essential, the korban pesach (consisting of barbequed lamb chops) is brought solely for the purpose of eating, as we celebrate Jewish nationhood at the seder. We can thus readily understand why the Gemara rules that one may slaughter the korban pesach on behalf of a tevual yom. Generally, a person who was impure would go to the mikvah on the last day of their impurity—i.e., a person who came in contact with a dead body would go the mikvah sometime on the seventh day. As soon as nightfall arrived, they would automatically be purified, allowing them to eat from sacrificial meat or enter the Temple.
While one may slaughter the korban pesach with a tevul yom in mind—as such a person will become pure automatically—one may not slaughter the korban for someone who we anticipate will go the mikvah later that day, but who has yet to do so at the time the korban is slaughtered. We are afraid that, notwithstanding the best of intentions, they may not actually make it to the mikvah.
Thus, it comes as somewhat of a surprise to learn that one may slaughter the korban pesach for "one for whom it was promised that he will be released from jail" (Pesachim 91a). Why are we not afraid that a delay may happen in this case? The Gemara's answer is simple and profound. "The remnant of Israel shall not do iniquity, nor speak lies; neither shall a deceitful tongue be found in their mouths"(Tzephania 3:13). A Jew may sin, but a Jew does not lie. The Talmud teaches that "the signature of G-d is truth" (Shabbat 55a), and when one speaks a mistruth, one defiles the image of G-d in which he was created.
Of course, such a statement may make for a pious-sounding sermon, but tragically it does not seem to reflect reality. It is for this reason that the verse begins, "the remnant of Israel". If one wants to remain a remnant of the Jewish people—and considering that we have been around for 4,000 years and there are fewer than 14 million of us, we are little more than remnants—one must ensure that one speaks only the truth.
Children are brutally honest—sometimes embarrassingly so. The best way to turn them away from Judaism is with mistruth, hypocrisy and deceit.
Our nation was founded on Pesach, but will endure only through the absolute fidelity to truth.
 The rule that one may go to the mikvah only after nightfall is specific to a woman who is a Nidah.
 This law serves as the background to the first Mishnah of the entire Talmud: "From when may one begin to say shema in the evening? From the time the kohanim enter to eat terumah (Brachot 2a)". Kohanim who were impure were forbidden to eat terumah, the special tithe (approximately 2% of the produce) separated by the Israelite farmer. To ensure that the kohanim could eat terumah at the first possible moment, they would go to the mikvah during the day and await the onset of nightfall. In the days before clocks, the eating of terumah by the kohanim served as a signal to all that it was night, and time to say the shema.
 While halacha allows and even mandates untruths in certain limited circumstances, those have as their goal an even higher value—peace. Truth at times requires a non-literal expression.