University spokesman Chris Cook says campus police made a student welfare check and -- upon entering the room -- found evidence of drugs and drug paraphernalia.
The suspect, identified as Hollis Daniels, was taken to the campus police station for standard debriefing. Cook said Daniels pulled out a gun and shot an officer in the head, killing him.
"During this time, the suspect pulled a gun and mortally shot an officer," Texas Tech Police Chief Kyle Bonath said. "The suspect fled on foot and later apprehended by ... (campus police) near the Lubbock Municipal Coliseum."
ORIGINAL REPORT: Texas Tech on lockdown after shooting
Texas Tech on lockdown after reported shooting
Texas Tech officials initially issued a lockdown alert to students on social media, urging those on campus "to take shelter in a safe location."
"The family of the officer is in the thoughts and prayers of the Texas Tech community," said Texas Tech President Lawrence Schovanec. "I want to express my deep appreciation to the Texas Tech Police Department, Lubbock Police Department, Lubbock Sherriff's Office, and other state and federal law enforcement officials for their response."
Texas Gov. Greg Abbott also issued a statement about the shooting late Monday, saying "hearts go out to the family of the police officer killed." Abbott also said he had mobilized state law enforcement resources to aid in the investigation.
The Associated Press contributed to this report.