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Seder Karban Pesach: The details of the Pesach offering are to be read after Mincha of Erev Pesach, as written in the Siddur. It is to be read before sunset. [If it was not read before sunset, it is to be read until nightfall.] The detailed laws of the Karban Pesach are read in preparation, and in correspondence, to the original Pesach offering, as the verse states that the service of the lips takes the place of the sacrifice. Thus, every G-d fearing Jew is to beware to read it on time, and is to be pained by the destruction of the Temple and supplicate to Hashem that the Temple be rebuilt speedily in our days. [The Rebbe Rashab was accustomed to recite it while standing facing south.]
Pesach Erev Shabbos: When Pesach falls on Erev Shabbos, one is to recite Hodu and Patach Eliyahu before Mincha.
 Siddur Admur “Bizmano”; see Hisvadyus 5748, p. 448; Likkutei Sichos 32 p. 36-43
 The reason: As Mincha corresponds to the afternoon Tamid offering which was brought prior to the Pesach offering. [Admur ibid]
 As according to some opinions, one may bring the Karban Pesach until nightfall.
 Likkutei Dibburim p. 1367