Nicholas Poehl and Robert Barfield tell Eyewitness News it does not appear that Dimitrios Pagourtzis was targeting anyone in the shooting two weeks ago.
The attorneys said Friday that Pagourtzis has yet to undergo a mental health evaluation, but the professional who will conduct that review has been selected.
Last week, Poehl told ABC13 that the suspect didn't remember much of what happened on May 18.
Pagourtzis remains in solitary confinement in Galveston County Jail, where he has been permitted to receive two 20-minute visits in jail each week.
The suspect's parents, Antonios Pagourtzis and Rose Marie Kosmetatos, have both been to the jail to visit their son, the attorneys said.
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