There are plenty of Catholic parishes totally allergic to the use of Latin. You get the impression they would come out in hives if you just said "in nomine Patris…" Nevertheless, even in such parishes, the original language of the "Lord have mercy", the Greek "Kyrie eleison", is often used.
Kyrie eleison consists of a vocative, Kyrie, followed by an aorist imperative eleison. The vocative is the case for addressing someone. "The Lord sits on high" – "the Lord" is in the nominative; but "Lord have mercy" – "Lord" is in the vocative since he is being addressed or called on (Latin voco I call). In the indicative mood (the mood used for the verb in basic statements or questions – and for present purposes I am restricting this account to theGreek of the New Testament) the default tense is the present. Outside of the indicative, for example in the imperative (where we give orders) the default tense is the aorist. In the indicative the aorist is typically about past time, it is the equivalent of the English simple past (he went there). In Greek, the aorist indicative modifies the beginning of the verb with an augment (usually a short e) which shows that the verb is about the past. In the imperative the aorist has no reference to the time when something takes place or the length of time it takes to occur. For this reason the aorist imperative does not have an augment
We write "Kyrie eleison" in English texts because that is how it is spelt in Latin texts. In Greek it is Κύριε ἐλέησον which might (I stress might) be more accurately transliterated "Kurïe eleēson". The exigencies of Roman pronunciation of Greek led to the spelling we use. The aorist imperative is a bit abrupt. It is the way one addresses a servant. The possible rudeness of this construction when addressing the Almighty might be explained by remembering that each time we are asking for mercy, we do so because we actually need it right now – not that we are fine for the moment but keep the mercy coming just in case.
ἐλέησον looks like it has an augment (ἐ/e) which is confusing since the ending is an imperative. But don't (as I said above) aorist imperatives lack the augment? They do and in this case the ἐ is not an augment but part of the stem of the verb ἐλέεω "I have mercy on, show pity to". The aorist indicative "I had pity" is ἠλέησα ēleēsa. In this verb past time is indicated by "stretching" the initial "e" so that it becomes long.
When I was teaching Greek I pointed my students to the Eleemosynary Office(s) (search Eleemosynarius and see here) of the Holy See which carry out the Pope's charitable activities to help them remember that ἐλέησον comes from a verb that begins with an epsilon (ε).
Of course that depends on being familiar with that institution. (It is the source of Papal blessings which people give newly weds or couples on their major anniversaries and so on). To Dr Rod Decker (due respect, due respect) of the Baptist Bible Seminary it is an entirely new word. The article he links to is very interesting.