Can we terminate an employee who lied about threats from other coworkers?

Employer here. A depressed, mentally unstable employee (confirmed medically) recently yelled at another employee over a disagreement regarding politics and religion. The second employee yelled back. The instigating employee then texted management claiming the second employee had threatened his life. A witness who was there at the time said this is not true and nothing of the sort was said. The instigating employee refuses to work with the second employee because he now 'fears for his life.' The second employee has been a model employee for 30 years, no complaints or write ups. The instigating employee has been employed for two years and recently began a new medication that has caused severe attendance and reliability issues. The instigating employee walked off the job after the argument - combined with his terrible past attendance = grounds for termination. However, we are worried that firing him now may be perceived as retaliation for him reporting perceived harassment. We feel his behavior is a risk to customers and employees and that his terrible attendance record was grounds for termination anyway. Can we fire him for his attendance issues, even though his most recent job abandonment occurred after his perceived threat on his life? The situation is he said/she said, and the only witness says there was nothing remotely close to a threat made that day. The instigating employee may claim that the termination was a result of his homosexuality and personal beliefs, as an argument about the topics caused the misconduct to occur.