The Problem: An apparent mistake in aliyot.
(יד) הֲיִפָּלֵ֥א מֵיְהוָ֖ה דָּבָ֑ר לַמּוֹעֵ֞ד אָשׁ֥וּב אֵלֶ֛יךָ כָּעֵ֥ת חַיָּ֖ה וּלְשָׂרָ֥ה בֵֽן׃
(14) Is any thing too wondrous for the LORD? At the set time I will return unto thee, when the season cometh round, and Sarah shall have a son.’
This pasuk marks the end of Rishon. But it is really the end of the narrative?
(טו) וַתְּכַחֵ֨שׁ שָׂרָ֧ה׀ לֵאמֹ֛ר לֹ֥א צָחַ֖קְתִּי כִּ֣י׀ יָרֵ֑אָה וַיֹּ֥אמֶר׀ לֹ֖א כִּ֥י צָחָֽקְתְּ׃ (טז) וַיָּקֻ֤מוּ מִשָּׁם֙ הָֽאֲנָשִׁ֔ים וַיַּשְׁקִ֖פוּ עַל־פְּנֵ֣י סְדֹ֑ם וְאַ֨בְרָהָ֔ם הֹלֵ֥ךְ עִמָּ֖ם לְשַׁלְּחָֽם׃
(15) Then Sarah denied, saying: ‘I laughed not’; for she was afraid. And He said: ‘Nay; but thou didst laugh.’ (16) And the men rose up from thence, and looked out toward Sodom; and Abraham went with them to bring them on the way.
The Sodom narrative is placed in Sheni, Shlishi, and half of Revi'i. What, then, is the underlined pasuk doing at the beginning of the second aliyah?
(מט) הִנֵּה זֶה הָיָה עֲוֹן סְדֹם אֲחוֹתֵךְ גָּאוֹן שִׂבְעַת לֶחֶם וְשַׁלְוַת הַשְׁקֵט הָיָה לָהּ וְלִבְנוֹתֶיהָ וְיַד עָנִי וְאֶבְיוֹן לֹא הֶחֱזִיקָה.
(49) Behold, this was the iniquity of thy sister Sodom: pride, fulness of bread, and careless ease was in her and in her daughters; neither did she strengthen the hand of the poor and needy.
The reason why Sodom was so terrible was that it sinned unabashedly, never losing its sense of haughty pride. The reason that Sarah's denial is included in the Aliyah is to provide contrast, seeing as she isn't proud of sin and fears Hashem.
Side point/source:
(ג) וַיִּמָּנְעוּ רְבִבִים וּמַלְקוֹשׁ לוֹא הָיָה וּמֵצַח אִשָּׁה זוֹנָה הָיָה לָךְ מֵאַנְתְּ הִכָּלֵם.
Notice the ending of the pasuk: Judah refused to feel ashamed by sin. To what is this compared by the pasuk? To the forehead of a harlot, hinting back to Sodom:
One last insight to sum it all up:
(כ) יְהוּדָה בֶן תֵּימָא אוֹמֵר... עַז פָּנִים לְגֵיהִנָּם, ובשֶׁת פָּנִים לְגַן עֵדֶן. יְהִי רָצוֹן מִלְּפָנֶיךָ יְיָ אֱלֹהֵינוּ שֶׁתִּבְנֶה עִירְךָ בִּמְהֵרָה בְיָמֵינוּ וְתֵן חֶלְקֵנוּ בְּתוֹרָתֶךָ:
(20) Yehudah Ben Teima says:... The strong-faced go to Gehinnom (Heck) , and the shame-faced go to the Garden of Eden. May it be Your will, Hashem our God, that You build Your city speedily in our days and give us our share in Your Torah.