Not all lies by New Orleans police officers are capital offenses, it turns out.

A veteran officer who was fired in 2013 after he called in sick so he could sell funnel cakes at a Lundi Gras celebration must be reinstated to the force with back pay because the Police Department failed to prove he violated the department’s “you lie, you die” policy, the city’s Civil Service Commission has ruled.

The commission found that department brass arbitrarily applied the policy, instituted in 2011 by former NOPD Superintendent Ronal Serpas, seemingly as “an afterthought” in firing Officer Gary Lee in June 2013.

It affirmed that the 28-year veteran violated several NOPD policies and was rightly suspended for calling in sick after a supervisor refused his request for a furlough day.

Lee was found on Feb. 11, 2013, working at the “Team Funnel Cake” tent at Woldenberg Park on the river, for a business he ran with his wife. He had called in sick that morning, although he was scheduled to work in uniform on a Carnival parade route.

NOPD policy bars officers from working elsewhere when they claim illness, and in any case, Lee hadn’t submitted the proper paperwork to be working an outside job, the department found. The commission upheld a 22-day suspension for him. But in a 16-page ruling this month, it noted that Lee readily admitted calling in sick so he could sell his tasty treats, never denying that his claim of illness was bogus.

And it ruled that department brass couldn’t adequately explain just what lie had prompted Lee’s firing.

Either he was fired for calling in sick when he wasn’t, in which case NOPD policy spells out a suspension of one to 30 days, or else he lied when he purportedly claimed that he had submitted proper paperwork for outside employment years earlier.

In that case, the commission found, the department failed to make the allegation clear, leaving Lee with no fair shot to defend himself.

Testimony by NOPD higher-ups at a hearing on Lee’s firing was “confusing and muddled,” the commission found. It ordered that he be reinstated “with all back pay and emoluments.”

Follow John Simerman on Twitter, @johnsimerman.