How could Lavan claim "Lo Ye'aseh Kein bi'Mekomeinu ..."? Did he not know that when he made the agreement with Yakov?
Targum Yonasan: Refer to 29:22:1:1**
Tosfos ha'Shalem (1, citing R. Efrayim): Lavan said that he assumed that Yakov knew the custom, and intended to marry Leah first.
Rosh (18): They agreed about "Bitcha ha'Ketanah." Lavan said that this is Leah, who is shorter (Yefas To'ar is stature).
Tosfos ha'Shalem (30:9:3, citing R. Efrayim): Lavan said "I intended to give Leah to Esav, the Bechor. Now I learned that he sold the Bechorah to you, so it was proper to give Leah to you."
If one was Mekadesh "your daughter" and did not specify which, we do not say that surely, the father gave the older (Kidushin 52a)!
It seems that "we do not give the younger before the older" is not a universal custom. 1 (See Tosfos 52a DH v'Hilchesa.)
However, the Rashbam (Bava Basra 120a DH l'Halan) explains that presumably, Benos Tzelafchad married in order of their age, and the Bach and Shach (YD 244) bring this l'Halachah.