Llamas moved to the United States as a teenager. He played for two years at Pima Community College in Tucson,Arizona, where he earned Arizona Community College Athletic Conference All Conference honors his Freshman and Sophmore seasons. Instead of attending an NCAA college, like most NBA players, Llamas chose NCAA division II Grand Canyon University where he earned NCAA division II player of the year during his Senior season.

Llamas had already made a mark on Mexican basketball when he graduated from Pima Community College: Having played in the Mexican league many years, he was named the Mexican national team's starting center, and he participated in such international events as the 1993 Central American and Caribbean Games, held in Ponce, Puerto Rico.

When Llamas played at Pima Community College, he played well enough to make Phoenix Suns scouts feel impressed. In 1996, he was signed by the Suns. When he made his Suns debut, he made history by becoming the first Mexican to participate in an NBA game.

Llamas had an impact in the Phoenix community, partly because of the large amount of Hispanics who live there. Soon after he began playing with the Suns, he was featured on the cover of the Suns' magazine, Fastbreak. Hoping to keep on bringing Hispanic fans to their home games, the Suns acquired Puerto Rico's Daniel Santiago soon after Llamas was released.

Llamas played in 20 games during his debut season, scoring 34 points for an average of 1.7 points per game, with 18 rebounds for 0.9 rebounds per game and 4 assists, for 0.2 assists per game.

During his second season, in 1997-98, he played in eight games, scoring 24 points for a total of 3.0 points per game, with 18 rebounds for a total of 2.3 rebounds per game, and 1 assist, for 0.1 assists per game.

After 28 games in two seasons with the Suns, Llamas was released. His production totals may have been adversely affected by his not playing many minutes as a member of the Suns: in his 28 games, he only saw action a total of 143 minutes, for an average of 5 minutes played per game. On the other hand, local newspapers reported during his stint that his conditioning was said to be poor, at least initially.

Llamas continued on playing basketball, playing in various international leagues as well as in the Mexican league. He participated at the 2000 Summer Olympics in Sydney, Australia, alongside Eduardo Nájera, among others.

In 2004, Llamas tried to make a comeback to the NBA with the Milwaukee Bucks. The Bucks had Santiago playing at center, however, and they decided not to sign Llamas.