Is it permissible to say "May our Lord preserve you" to unhostile Christians in daily and business interactions, and does this fall under the prohibited supplication for them to have a long life?

The phrase "Allah yakhleek" (May Allah keep you) is intended to mean permanence of being or preservation. Some scholars have prohibited praying for a Christian or a non-Muslim for a long life. Among them is what Al-Athram narrated from Abu Abdullah, who permitted writing "May Allah keep you, protect you, and grant you success" to a Christian. It was also narrated from the Salaf that whoever prays for a oppressor to remain (alive) has loved for Allah to be disobeyed. Some have allowed praying for a disbeliever for a long life due to the benefit it brings to Muslims through the jizya (poll tax), while others have deemed it impermissible. The more appropriate approach is to pray for their guidance, as it is authentically reported that the Messenger of Allah, peace be upon him, prayed for the guidance of Daws and Thaqif, and he used to say to the Jews when they sneezed, "May Allah guide you and set your affairs aright."