Concerning Owen's "Dulce et Decorum Est," strictly speaking, the final lines of the poem, which we can translate as "Sweet and fitting it is to die for one's country," do not constitute irony in the poem, since the speaker writes that his "friend" should not tell the lines to children.
In other words, if the Latin lines concluded the poem without the disclaimer, they would be ironic. Since they are prefaced with the suggestion that if the "friend" understood the truth about war, he would not speak the lines to children, the lines are not ironic.
Owen once referred to this poem as a "gas poem." The poem details many horrors of warfare, but primarily deals with the use of poison gas, a weapon introduced in large scale during WWI. Poison gas is a particularly horrible weapon, as the poem reveals. WWI brought about the use of numerous "advancements" in weaponry, including the use of tanks and airplanes, as well as poison gas, as weapons. Warfare changed forever during WWI, and certainly is substantially different from Horace's day (the writer of the two Latin lines).
If, after detailing the horrors of warfare in WWI, including the use of poison gas, the speaker of the poem had concluded the poem with Horace's line--sweet and fitting it is to die for one's country--then certainly he would be using the lines ironically. They would constitute a use of irony. There is nothing sweet and fitting about dying from inhaling poison gas.
But, the speaker tells his "friend" that if he understood the truth about war, he would not tell these lines to children.
Here are the final lines of the poem:
If you could hear, at every jolt, the blood
Come gargling from the froth-corrupted lungs,
Obscene as cancer, bitter as the cud
Of vile, incurable sores on innocent tongues,--
My friend, you would not tell with such high zest
To children ardent for some desperate glory,
The old Lie: Dulce et decorum est
Pro patria mori.
From the outside looking in, so to speak, I can look at what Horace wrote and look at what Owen writes, and say that, yes, it is ironic that Horace would say it is sweet and fitting to die for one's country when war is what Owen reveals it to be. Also, the speaker is, indeed, pointing out to the "friend" the irony of his, or anyone's, believing war is noble and glorious. War is the opposite of noble and glorious and sweet and fitting.
But, again, strictly speaking, since the speaker warns against using the sweet and fitting lines, he is not being ironic when he writes them. He is not writing them as if they are true, while meaning the opposite. The speaker is directly writing that if one knew the truth, one would not use them.
This whole poem is an attempt to convey an anti war sentiment. This makes the final lines (the quote in Latin) ironic because those lines are most definitely not anti war.
The idea behind the quote is that there is something "sweet and right" about dying for your country. To die in this way is glorious, according to Horace's lines. But the whole rest of the poem is exposing the ways in which fighting and dying in this modern war is anything but sweet and right.
In the rest of the poem, Owen is describing the complete horror of the battlefield in WWI. The modern way of war has made it so that Horace's words can only be ironic -- there is no glory left, there is nothing right about this war (assuming there ever was anything sweet and right about war...).