FITCO's director has said the men apparently had been helping Routh work through post-traumatic stress disorder.
Kyle, Littlefield and Routh arrived together at the Rough Creek Lodge shooting range, about 50 miles southwest of Fort Worth, authorities say. Routh later fled in Kyle's truck and went to his sister's home.
According to a search warrant, Routh told his sister and brother-in-law that the men "were out shooting target practice and he couldn't trust them so he killed them before they could kill him." Routh's sister called the police, describing her brother as "psychotic." Routh was arrested after a short police chase.
Routh's brother-in-law told authorities that Routh had recently been diagnosed with PTSD.
One of Routh's attorneys, J. Warren St. John, said his client had been released from the Dallas Veterans Affairs hospital against his family's wishes just two days before the shootings.
Littlefield's funeral was held Friday in Midlothian. Afterward, Littlefield's relatives said the outing with Routh was intended to be therapeutic.