It is typical for a king to declare himself formally. In this case Limhi's declaration relied upon lineage. It is interesting that the declaration of lineage also required the connection to Zarahemla, for that is probably where their ultimate authority came from. Remember that at this time Limhi does not appear to know that his captives are also from Zarahemla, so his statement to Ammon is not one of recognition of commonality, but rather of declaration of connection to a seat of power.
This is a known practice from later Mesoamerican peoples. Those who had moved from one area to another found it necessary to trace their ultimate authority to a remote. but established lineage. The Chakchiquel specifically receive their authority for Nacxit, the ruler in Tollan: "the Lord Nacxit said:
"Climb up to these columns of stone, enter into my house. I will give you sovereignty…" (_Annals of the Cakchiquels._ Tr. Adrian Recinos and Delia Goetz. University of Oklahoma Press, 1974, p. 65). Neither the Popol Vuh nor the Title of the Lords of Totonicapan for the Quiche mention sovereignty directly, but both trace their foundational lineages to events in Tollan (_Popol Vuh_. Tr. Dennis Tedlock. Simon and Schuster1985, 171-176; "Title of the Lords of Totonicapan." In: _Annals of the Cakchiquels._ Tr. Adrian Recinos and Delia Goetz. University of Oklahoma Press, 1974, p. 169-171).