Lyxen
Great Old One
The wording of Zone of Truth says that it detects a "deliberate lie". Deliberate means "intentional." Since a creature compelled to knowingly lie is not doing so voluntarily, I would rule that Suggestion could loophole Zone of Truth. Even if the creature is well aware that they are lying, the lie is not deliberate on their part - it's compelled.
The simple fact that you have to change the word used in the description of the spell to try and prove a point shows that this simply is not the intent of the spell.
When someone is compelled by suggestion for an action, the action is certainly deliberate.
As a DM, I would allow this tactic to succeed but the Suggestion spell would have to be worded carefully. "Ray, when someone asks you if you're a god, you say YES!" would work.
And it would still absolutely be a lie.