The 34-year-old was married and had children, and had just moved to Killeen, Texas, from another military post in February.
Lopez opened fire on the base Wednesday afternoon, killing three people and injuring 16 others before turning the gun on himself.
Officials said they don't know his motive.
"There are initial reports there may have been an argument in one of the unit areas," Lt. Gen Mark Milley, the post's commanding general said. "Obviously, we are digging deep into his background, any criminal or psychiatric history, his experiences in combat. All of the things you would expect us to do are being done right now."
Lt. Gen. Mark Milley, in a news conference late Wednesday night, said Lopez had been under evaluation for a possible diagnosis of post-traumatic stress disorder.
"He was not diagnosed, as of today, with PTSD," Milley said.
Lopez was being treated and medicated for depression, anxiety and various other psychiatric complaints, and had a "self-reported" traumatic brain injury suffered while he was deployed in Iraq for four months in 2011.
Milley said there were no records Lopez had been injured while on tour.
Lopez reportedly had little to no social media presence on the Internet.