Both Noxus and Zaun armies were extremely busy fighting in the invasion of Ionia. We know as a confirmed fact that all their major military forces were locked in that war, seeing as people involved in the invasion include Singed, Warwick and Riven, which likely also means the rest of their military force.
Now, let us look at the world map.
There it is.
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Demacia and Piltover are in the direction opposite from Ionia as far as Noxus and Zaun go. In fact, the only major landmark between Demacia and Piltover is the Institute of War.
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The passage through the Guardian's Sea leads within maybe a week's travel from Bilgewater, meaning those areas would be actively patrolled by pirate crews looking to profit off passing merchants.
Without the Institute of War inhibiting Demacia's progress and keeping both it and Piltover in check, the tactical layout behind the Noxian invasion of Ionia is, to put it mildly, embarrassing. Noxus's alliance with Bilgewater is more guidelines than hard rules. The supply ships heading between Noxus and the Ionian front lines would be easy pickings for Bilgewater pirates and would come under attack badly, leaving Noxus's military stretched between Ionia, guarding the city and providing armed-to-the-teeth convoys for their supply routes. As a result, nothing would stop Demacia from simply charging at Noxus from the rear, smashing through the severely diminished forces and razing the city.
A neutral third party to keep Demacia in check is literally the only thing that would keep Noxus from being completely demolished. It's not a strategy or an invasion, it's a deathwish.
Actualy the IoW prevented Demacia from acting fearing that due to the already high-tension between the two rival city states, it could case another war to emerge, also during said time Ionia was not yet part of IoW remaining as neutral faction, which is the exact reason why Noxus / Zaun wen rampage over (land controll). During / after the invasion Ionia got accepted on IoW however the damage was already done and Noxus / Zaun possesed control of a nice chunk of land from Ionia.
The following events were: Karma / other ionian requested to join IoW and to allow em to fight Noxus (not Zaun if i recall) and if Ionia wins the army stationed could leave Ionia alone, on Case of Defeat Noxus could remain under controll of the claimed land and Ionia could be prevented from requesting anothe batle for the next 10 years.
Ionia won and noxus recalled, Riven, which was a soldier under singed wing, after watching her brethen (allies) and enemies dying to singed weaponn (poison and much other tuff from Zaun) betrayed em and became na Exiled.
This is my knowledge so far.