Details of the escape were sketchy although Clark said officers realized during a routine inmate count that the two had disappeared. He said the pair had been accounted for earlier Tuesday.
They were believed to have fled on foot through a cut fence, Clark said.
Dilley also is about 80 miles northeast of Laredo, which is on the Texas-Mexico border, and Clark said he thought the two may have headed toward the border.
"We're still trying to get information," Clark said. "We have a large contingent of corrections officers and law enforcement in the area searching for these two individuals."
Bustos-Diaz was serving 35 years for murder in Harris County. Lopez, who was convicted in Hidalgo County, was serving 20 years for two counts of aggravated kidnapping and 12 years for possession of cocaine and possession with intent to deliver cocaine.
Bustos-Diaz pleaded guilty in July 2006 to beating, stabbing and cutting the throat of Deborah Kay, who was his boss at a Harris County horse stable where she lived. Court records show that in a statement to detectives, Bustos-Diaz said he became angry when Kay turned down his request for a day off work. Her body was found Jan. 30, 2005, on a bedroom floor.
Harris County sheriff's investigators said Bustos-Diaz also suffered a hand injury during the attack and his blood was found on about $600 in cash. The knife used to kill the woman was recovered along with his bloody clothing.
The Briscoe Unit, in operation since 1992, is on more than 400 acres in Frio County just west of Dilley and about a quarter-mile west of Interstate 35. It has a capacity of 1,342 inmates.