Lilium has an even bigger impact if you contrast the lyrics with the manga - because unlike the anime, the manga shows themes like: “what’s even a human being?”, “does evil come from nature or nurture?”, “is redemption even possible?”.

…and the lyrics are basically a prayer for redemption, I’ll coarsely translate them here:

The mouth of the just will repeat wisdom
And his tongue will utter the evidence (i.e. declare judgment)
Blessed the man who endures temptation
Since he was tested, he'll get the crown of life

Oh Lord, [you are the] source of goodness
Oh Lord, [you are] divine fire, have mercy [of us]

Oh, so holy, so serene
So benign, so delightful, the one believed to be the Virgin (Mary)
Oh, so holy, so serene, so benign, so delightful
Oh, lily of chastity

It fits perfectly once you identify Lucy with the sinner: she knows she’s guilty, and she’s asking God for redemption. With Kouta intervening in her favour, always showing compassion, much like the Virgin Mary would do in Christianity.