I guess you could call your struggles against Team Plasma a war, or indeed the fight between cloned and original Pokemon in the 1st movie (although that was more of a battle).
He's referring to the war he fought in, not some actual Pokemon World War.
Anyway, that's someone's theory from the Serebii forums; this seems to be the most likely explanation of Lt. Surge's talk of war. There's no other mention of it by anyone else, so I think this was an isolated affair, rather than anything large scale.
There has been a 'war', which is the one between the brothers who controlled Zekrom and Reshiram, who were the sons of the king (who coincidentally was the kinda-sorta-unofficial owner of Victini)
However, one day, the twin sons of the king—the Hero of Truth, who controlled Reshiram, and the Hero of Ideals, who controlled Zekrom—began a war over their beliefs.
This is the only one I can think of. This isn't the one Lt. Surge refers to, because it happened a 1000 years ago. Otherwise, Surge is looking pretty good for someone over 1000.