Sooo I bought the Yuri!!! on Ice OST and the booklet includes the lyrics of all the songs (the ones with lyrics obviously). I’ve been curious about Agape from the very beginning so I’m posting the lyrics here in case anyone else was curious:
Sic mea vita est temporaria, cupit ardenter caritatem aeternam
Et denique aperiens fores occultas, nobis, grandis et clara nosque curabit nobis, grandis et clara nosque curabit
magna, magna, caritas Ah! Audio vocem tuam! Adest mi libertas!
Mea vita amabit, caritatis pacem. Hanc felicitatem aeternam esse oro.
Also, my father teaches Latin, so I asked him to help me translating them. I must say this is not a very good translation. I don’t know if the lyrics really make complete sense in Latin (I found some incongruities in lyrics of the songs in English, so who knows with Latin; my father said some of them were a bit weird). Also, my father helped me translating to Spanish and then I translated that to English, so I’m sure this is not the best translation you could get. The booklet also included a Japanese translation, which I couldn’t 100% understand, but from what I could I’d say it’s not completely literal either. Still, this may give you a general idea of the meaning, at least:
Although my life is temporary, it yearns for a passionate eternal love
I will believe, I will give, I will hope, I will worship, I will work, I will show gratitude.
And finally opening hidden doors, to us, great and clear it will care for us to us, great and clear it will care for us
great, great, love Ah! I listen to your voice! I can grasp freedom!
My life will love, love’s peace. I pray for this happiness to be eternal.
I maintained the punctuation from the lyrics in the booklet (although my father was convinced that there’s something wrong with it). Also, as you probably have already deduced, the “love” referred to in the Latin lyrics (caritas) is a love with no sexual connotation, commonly (although not exclusively) used to refer to love for God.
EDIT: I was asked to provide the Spanish translation (which you can find here) and I added to it some nuances provided by the Japanese translation from the booklet, that I have finished studying. Here you have them in English:
Third stanza in Japanese is: 「ついには隠された扉は開かれ 大になる御心が現れて 清明な癒やしをもたらす」 Following this, I would translate this stanza more like And finally opening hidden doors, [God’s spirit will appear] before us, great and clear, [and] it will [heal] us
Forth stanza in Japanese is: 大いなる、大いなる神の愛が、 ああ、あなたの声が聞こえる 私はついに自由を手にしたのだ This is a little nuance but I would translate it like great, great [God’s] love Ah! I listen to your voice! I can grasp freedom!
Last stanza in Japanese is: この生は、この愛がもたらす平安 この幸せが永遠につづくようにと、私は祈る Considering this version, I would translate the stanza more like My life [will be dedicated to] the peace [that brings] this love. I pray for this happiness to be eternal.
I think the Japanese version makes more sense than the Latin one, and it helps a lot to understand things omitted in the Latin version. Still, remember that I’m not proficient nor in Latin nor in Japanese, so don’t take my interpretation as 100% reliable!