The Church’s teaching in Lumen Gentium 16 might be helpful here:
Finally, those who have not yet received the Gospel are related in various ways to the people of God. In the first place we must recall the people to whom the testament and the promises were given and from whom Christ was born according to the flesh. On account of their fathers this people remains most dear to God, for God does not repent of the gifts He makes nor of the calls He issues. But the plan of salvation also includes those who acknowledge the Creator. In the first place amongst these there are the Muslims, who, professing to hold the faith of Abraham, along with us adore the one and merciful God, who on the last day will judge mankind. Nor is God far distant from those who in shadows and images seek the unknown God, for it is He who gives to all men life and breath and all things, and as Saviour wills that all men be saved. Those also can attain to salvation who through no fault of their own do not know the Gospel of Christ or His Church, yet sincerely seek God and moved by grace strive by their deeds to do His will as it is known to them through the dictates of conscience. Nor does Divine Providence deny the helps necessary for salvation to those who, without blame on their part, have not yet arrived at an explicit knowledge of God and with His grace strive to live a good life. Whatever good or truth is found amongst them is looked upon by the Church as a preparation for the Gospel. She knows that it is given by Him who enlightens all men so that they may finally have life. But often men, deceived by the Evil One, have become vain in their reasonings and have exchanged the truth of God for a lie, serving the creature rather than the Creator. Or some there are who, living and dying in this world without God, are exposed to final despair. Wherefore to promote the glory of God and procure the salvation of all of these, and mindful of the command of the Lord, “Preach the Gospel to every creature”, the Church fosters the missions with care and attention.
I’m not aware of an explicit teaching on asking Mormons or JWs to pray for an intention, but from the the above, it would seem to be permissible - their faiths, being in some way both a “preparation for the Gospel” - where they have truth and “a lie” of “the Evil One” where they are false. Thus, I’d wager to say it is permissible, but I couldn’t recommend it. Besides, it might give the Mormon or JW the feeling that you, as a Catholic, approve of their odd notions of God. Lastly, I couldn’t imagine St. Athanasius asking Arius to pray for him. As both the JWs and Mormons seem closely aligned with Arianism, I’d pass. But again, that’s just me. I don’t believe the Church forbids it.