Night-night!

וַיָּקָם פַּרְעֹה לַיְלָה, הוּא וְכָל-עֲבָדָיו וְכָל-מִצְרַיִם, וַתְּהִי צְעָקָה גְדֹלָה, בְּמִצְרָיִם: כִּי-אֵין בַּיִת, אֲשֶׁר אֵין-שָׁם מֵת. - 30 - And Pharaoh rose up in the night, he, and all his servants, and all the Egyptians; and there was a great cry in Egypt; for there was not a house where there was not one dead.

וַיִּקְרָא לְמֹשֶׁה וּלְאַהֲרֹן לַיְלָה, וַיֹּאמֶר קוּמוּ צְּאוּ מִתּוֹךְ עַמִּי--גַּם-אַתֶּם, גַּם-בְּנֵי יִשְׂרָאֵל; וּלְכוּ עִבְדוּ אֶת-ה', כְּדַבֶּרְכֶם - And he called for Moses and Aaron by night and said: 'Rise up, get you forth from among my people, both ye and the children of Israel; and go, serve the Lord, as ye have said.
(12:30-31)

As made abundantly clear by the bold letters, there is a repetition of the time the sequence of events that took place in light of the imminent arrival of the 10th plague. If Paroh only wanted to tell them to "rise up and go forth from among my people", then there was no need to repeat that this occurred at night, as obviously it is established from the previous Pasuk that this is the case. So why the repetition?

An intriguing answer by the Griz, R' Yitzchak Ze'ev Soloveitchik (biography here) and the Ohr Hachayim, R' Chaim ibn Attar (biography here) that shows how the various Psukim link.

The previous time that Paroh had met Moshe and Ahron, their meeting did not go well. It (10:28) concluded וַיֹּאמֶר-לוֹ פַרְעֹה, לֵךְ מֵעָלָי; הִשָּׁמֶר לְךָ, אַל-תֹּסֶף רְאוֹת פָּנַי--כִּי בְּיוֹם רְאֹתְךָ פָנַי, תָּמוּת - Pharaoh said to him, "Go away from me! Beware! You shall no longer see my face, for on the day that you see my face, you shall die!"' Pretty bad meeting, but it got worse. After his final prophecy after this event, the Pasuk (11:8) says וַיֵּצֵא מֵעִם-פַּרְעֹה, בָּחֳרִי-אָף "And he went out from Pharaoh in hot anger." In Zevachim 102a Resh Lakish explains that this means that Moshe slapped Paroh.

With their prior meeting fresh in his mind Moshe would understandably have been loathe to see Paroh, "for on the day that you see my face, you shall die". If they hear him calling them, they weren't going to come running.

Paroh understood this, and shouted "לַיְלָה"!! "It's night-time!". His threat had been "for on the day that you see my face, you shall die", and perhaps was suggesting that he did not want to see them by day, but by night it was different.

So to answer our original question of why לַיְלָה is repeated, the answer is, it isn't! If we add punctuation:

"!וַיִּקְרָא לְמֹשֶׁה וּלְאַהֲרֹן "לַיְלָה - And he called Moshe and Ahron saying "It's nighttime!"- {my threat isn't relevant now!}

So in fact, the second time isn't a description of the setting, it is actually what he said!