I think of this in terms of personal salvation. Lucifer is like a force of nature. If he is truly the one you feel you must forgive or come to peace with to attain the blessings of the atonement, then by all means do so, and pray for him directly. Even just thinking about this may be a prompting that you need to do so, even if just in your own personal prayers. But for me I know there are bigger fish to fry, and they are in my life right now. I never really viewed it as Lucifer is the Almighty Evil Force without which we would all be angels dressed in blue jeans and t-shirts wandering around doing good to others all day. I also never viewed him as God's "muscle", who steps in to torture us because God with his white cotton gloves could never get his hands dirty that way, but hey, someone has to do it, right? I don't buy into that.
Rather I always viewed him as more symbolic, an example of what happens if we don't reconcile the natural man with the spiritual man and let pride run rampant in our lives. I am not sure I believe there is any real whispering occurring from his side to us, I think that again is more symbolism, and it really is about the inherent natural man in everyone that is predisposed to follow our passions, which we have been commanded to keep in check. It is about self-control, which is important in this life whether you adhere to a spiritual philosophy or not.
Learning self-control is, in whatever aspect you choose to view it, completely separate from religion, the toughest thing anyone will learn in this life. It is hard to tell yourself no, to tell yourself you can't have what you want right this moment, or even just to learn new things, and it's even harder to be open with yourself about things you need to change, which is why the vast majority of people won't ever really change, and why most people are depressed in one way or another at times in their lives, because it is depressing to realize that you are not controlling your life, or rather to know deep down you are not taking control of your life. But at the same time it is truly hard to take the kind of control, or exercise the self-discipline needed to take control. And sometimes other things are against us in this regard, some of us deal with chemical changes in our brains that make it harder to exercise self-control, or we make decisions that introduce outside influences, like alcoholism or drug addiction, or other things more subtle than that. The end result is we are buffeted by the prevailing winds of change, having no firm grasp on our natural inclinations, until we feel lost.
So back to a religious viewpoint, I think I have plenty of people right here right now I need to forgive, or learn to love as the savior commanded, and just don't have the time to waste worrying about whether the symbol of the resistance is just a misunderstood soul. Maybe when I have advanced sufficiently he will enter the picture again, if I ever reach that level. For now I am too focused on removing beams beyond measure from my own eye to worry much about Lucifer's eternal progression.
So that makes me wonder if maybe the Apostles do include him in their prayers to some degree. If nothing else at least to ask to soften his heart in our behalf to help us make it through this mortal sphere.
The extent to which we do already pray for Lucifer, as taught by the savior, is to ask for Heavenly Father's protection from his temptations. Well in a way that is asking for a blessing on Lucifer. After all we know that God does his work through love and patience and kindness, I mean it's not like when we pray for that God goes a gets a whip and 10 million strong angels to go whip Lucifer's *** into leaving you alone. As it says in D&C 121:
41 No power or influence can or ought to be maintained by virtue of the priesthood, only by persuasion, by long-suffering, by gentleness and meekness, and by love unfeigned;
42 By kindness, and pure knowledge, which shall greatly enlarge the soul without hypocrisy, and without guile—
43 Reproving betimes with sharpness, when moved upon by the Holy Ghost; and then showing forth afterwards an increase of love toward him whom thou hast reproved, lest he esteem thee to be his enemy;
So when we ask Heavenly Father to protect us from Lucifer's influence how does he do that? I would think he has to do it by showing Lucifer more love, by sending him H.F.'s spirit and softening his heart to help him not feel like he has to tempt us at that moment. To get a temporary stay he intercedes on our behalf in love and compassion.
Like if you have ever prayed for H.F. to soften someone's heart in your behalf, to help get a job, or a promotion, or get selected to a team, or get out of going to jail (I remembered this was trout posing the question =), when you generally pray to be protected from temptation you are asking H.F. to soften Lucifer's heart toward you.
But like Laman and Lemuel, Lucifer is not so easily swayed. He has lived among the angels and rejected the Spirit to God's own face, and fought with very real consequences (eternal damnation for 1/3 of God's children) and been cast out for so doing. His heart is pretty well hardened at this point. This is not a heart that softens easily. So the reprieve is temporary.
But still, in that prayer, you have prayed for Lucifer, in a way.