In 1758, a Lizama shows up for the first time in a Guam census (which we currently have). His name was Luis de Lizama and he is listed among the Pampanga soldiers. We know nothing more about him.
His wife was Teresa Ursula Sinia. Who she was and where she came from is not known. It is possible that Teresa was Chamorro and for the following reasons. First, although a good number of Spanish and Filipino soldiers brought wives with them, many did not and instead married Chamorro women. Second, there is another wife of a Pampanga (Filipino) soldier by the last name Sina. People were much more casual about spelling in those days, and Sinia and Sina could very well be the same last name. If so, they may have been sisters and it is less likely, though not impossible, that two sisters from abroad came to Guam as wives of soldiers. Finally, but probably most convincingly, Sinia/Sina could very well be the Chamorro word siña, which means "possible, able." Sinia/Sina is not a Spanish surname, that is more certain.
Whatever the case, the Lizamas of the Marianas seem to be one family, descended from Luis de Lizama who came to Guam in the 1750s if not before. By the time of the 1758 census he had four children, two boys and two girls.
The name itself is found in Spain and in her former colonies. But it is not extensive (like, let's say, Garcia or Fernandez). It's actually not very widespread at all. It seems to be a variation (again, clerks in those days spelled things the way it suited them) of Lezama. Even in the Guam census of 1897, Lizama is sometimes spelled Lezama, depending on who was the clerk writing the name.
Lezama is the name of a small village in Spain; in the Basque province of Vizcaya to be exact. Therefore, it's not Castillian but Basque, and scholars aren't certain of the meaning of the name. There is yet another hamlet named Lezama in the neighboring, and still Basque, province of Ålava.
How a soldier from Pampanga, Philippines got the surname Lizama is not known. Like many other Filipinos, he may have been mestizo himself; part-Filipino and part-Hispanic (whether Spanish or Latin American is unknown).
By the late 1800s, one or two Lizamas had served the local government, probably in more than one capacity. Chamorros were given local offices, such as neighborhood chiefs, supervisors of agriculture or livestock, justices of the peace and so on. They were then allowed to use the title "Don" which means, more or less, "Sir." There was one Don Hipolito Cruz Lizama in Hagåtña, married to Dolores Pangelinan. And one Don Joaquin Lizama, married to Vicenta Guzman. Don Hipolito was the head of one of the neighborhoods in Hagåtña. These neighborhoods were called "barangay" and the official was called the "cabeza de barangay." "Cabeza" literally means "head" in Spanish.
From Hagåtña, the Lizamas spread out to nearly every other settlement in the Marianas. By the late 1800s, there were Lizamas in Hågat and neighboring Sumay, and two Lizama teenage women in Inalåhan. One Jose Lizama moved to Luta (Rota) and probably married a Rotanese Chamorro woman with the last name Mundo. Several Lizamas moved to Saipan where the Lizama name is still going strong.
In the U.S. mainland, you're more likely to bump into a few Lizamas in California (370 people as of 2009) and in Texas (212 people), and I'll bet a good number of them will be Chamorro Lizamas, besides the Hispanic Lizamas.