The phrase "dulce et decorum est" is taken from the first line of the fifth stanza of Horace's Ode 3.2, a work that was widely studied in secondary schools in the original Latin in Owens' period and thus would have been familiar to his readers. The full phrase is:
dulce et decorum est pro patria mori
meaning that "it is sweet and proper to die for the sake of one's country". Part of the theme of Horace's ode, which is not really explored in Owen's poem, is that since death will come for us all eventually, it makes no sense to try to escape death by fleeing military service or other forms of cowardice.
The narrator refers to the phrase as the "old Lie" and obvious considers the warfare he describes so graphically as neither sweet nor noble. There are two reasons for this. The first was the shift in military technology, moving from individuals fighting with swords or lances to horrors of trench warfare and the use of chemical weapons. The second issue has to do with the way in which earlier poetry glamorized war without going into graphic detail about the pain and suffering and types of physical duress endured by soldiers.
Owen's narrator contrasts Horace's image of dying nobly with soldiers whose "blood/Come gargling from the froth-corrupted lungs". Thus the tone is one of bitter contempt and rejection of the phrase and all it stands for.