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A little prudence in all things:  Will I pray for JFK, yes, because I am told on good authority that he went to confession the day he was αssαssιnαtҽd.  If the Catholic Nancy Peℓσѕι dies tomorrow, will I say a rosary for her - No. I wish her to save her soul, but the circuмstances are far different.  

In the case of non-Catholics there is a different principle involved, especially if the person did not seem to make any movement toward the Church.  I know people were caught up with the whole "Charlie Kirk is a martyr" attitude after the assassination.  My take is, if Charlie Kirk went to hell, it was probably due to his utter stupidity, for marrying a woman who obviously had a shady, questionable past. 

I have a suggestion that is in accordance with the teachings of the Popes as AP graciously shared with us, and that will also satisfy piety. 

Use prayers for the holy souls in purgatory that have ecclesiastical approval. 

We are not supposed to be Protestants, who feel at complete liberty to pray totally in our own words, and as we please. Catholics are supposed to pray in the manner that Our Lord taught us, and according to the approval of the Church, as we can see in the prayers of Holy Mass, approved Catholic prayer books, the Divine Office, indulgenced prayers, and so on. 

Even in instances of mental prayer, we are taught by the saints and spiritual authors how to pray in our own words that is in a manner befitting Our Lord; with due humility and love, always with submission to the truths of our holy, Catholic Faith. 

The traditional Catholic prayer book of indulgences, The Raccolta from 1910 is available online, so I will here give some prayers that will satisfy the most ardent longings to relieve the Holy Souls in purgatory. https://archive.org/details/theraccoltaorcol00unknuoft/page/n373/mode/2up







For those who are concerned about saving those who are without the state of grace on their deathbed:

Instead of hoping that such souls ended up in purgatory, it would be far more useful to pray approved prayers for the dying on a daily basis, that they may be saved, even at the last hour. 

There is a two-volume work entitled "The Agonising Heart" (referring to the Heart of Jesus), by the Rev. Fr. Blot, 1869. https://archive.org/details/agonisingheart00blotgoog/page/n261/mode/2up

It contains ecclesiastical approval, and from p. 235 has devotions for the dying. I will give some of those prayers here.