Ramban: Pachad Yitzchak is Hashem's Midas ha'Din (A hint that He will punish Lavan severely if he transgresses - Ha'amek Davar).

Seforno: He was explaining that he appointed the god of Nachor together with the G-d of Avraham, because he was also the god of Terach, who was the father both of them. Ya?akov however, swore by Pachad Yitzchak feared, ¹ and Yitzchak was not the son of Terach.

Malbim: Lavan summoned Elokei Avraham, who knows hidden matters, to judge about them (Inuy), and Elohei Nachor, whom he thought supervises revealed matters, to judge open matters (war). He added Elohei Avihem, to justify Elohei Nachor, for he was also the god of Terach, the father of Avraham and Nachor. Ya?akov refused to combne another matter with Hashem, so he swore by Pachad Yitzchak - the Mitzvah of Kivud Av and his fear of his father.

Ha'amek Davar: The B?ris against war applied also to Lavan. He mentioned also Elohei Nachor, to demonstrate that he did not consider Elokei Avraham importanr, since he did not serve him. This pained Ya?akov, but to swear only in the name of Elokei Avraham would impinge on Lavan's Kavod. Therefore, he swore by Pachad Yitzchak - Refer to 31:53:151:2.

Oznayim la'Torah: Lavan referred to 'Elokei Avraham' - whose Midah was Chesed ² and who entered into a (positive) covenant with Avimelech and swore to him that they would do good to each other. ³ But that was not the gist of the covenant here, which entailed not doing harm to one another, ⁴ which was similar to the covenant that Yitzchak entered into with Avimelech. ⁵ Which explains why he swore by 'the G-d of Yitzchak his father'.

Oznayim la'Torah: Refer to Bereishis 21:24:1:2*; and 21:24:1:2**.

Moshav Zekenim: Perhaps Yaakov knew that [Nachor] did not serve idolatry (so Elokei Nachor is Hashem). ¹

Yaakov did not ask Lavan to swear. Lavan mentioned Elokei Avraham and Elohei Nachor on his own. Yaakov deviated, and swore by Pachad Yitzchak, to show his disapproval (based on Malbim, Ha'amek Davar).