This actually seems pretty straight forward. If the target of zone of truth knows it's lying (and fails the saving throw) it can't utter the lie - suggestion in effect or not.
Suggestion compels a target to pursue a course of action "to the best of its ability..." So the target will try to lie to the best of it's ability, even if compelled to tell the truth by zone of truth.
But if it knows it's lying, failing the zone of truth saving throw will prevent it from doing so (lying).
A better use of suggestion (as alluded to above) would be to suggest that a target answer a certain way if asked about something - for something it doesn't know is a lie.
If the target failed a saving throw for Suggestion to lie, and then failed a saving throw for Zone of Truth preventing them from lying, do you think their head would explode like in Scanners?