Yay, I get to dust off some old books!
Third and Second edition sources
The AD&D 2nd edition Faiths and Avatars supplement covers Kelemvor in detail. I'll be quoting from his entry from the more recent 3rd Edition Forgotten Realms book Faiths and Pantheons. It says this about him:
Cleric Alignments: LE, LG, LN
...
Kelemvor urges his clerics to act as stewards of the afterlife and to teach the people of Faerûn that death is a natural part of life. There is nothing to be feared in the transition, for only the truly wicked, the Faithless, or the False must fear the world beyond the Fugue Plane.
So this doesn't start well for you. While it's not against lying per se, he obviously wants Lawful alignments and doesn't want people to dwell in illusions: he's saying "just be real about it, you're going to die, it's going to happen, don't get all afraid of it, just live a faithful life and trust that whatever happens will happen." Note that being a chaotic cleric of his may be being False to their god.
After urging clerics to destroy all undead, it continues,
Kelemvor is a taciturn deity, and until recently was not completely sure of himself or his role. He has placed such uncertainties behind him however, and approaches his duty as a judge of the afterlife earnestly, tempering his strong sense of justice with kindness and forthrightness. He is not, however, particularly clever, and prefers to solve problems with direct action that sometimes leads to unintended results.
If you value forthrightness, you are not directly against lying as a form of dishonesty, but rather you have no patience for evasiveness or lies of ambiguity. So that limits the sorts of misleading to ones that are bold and direct, saying "Your enemy fled for Amn" when in fact he's staying in the local tavern. Similary he might have trouble with viewing your actions as unnaturally "clever" in a way he does not like: if, say, your GM introduces you to "Praewith, village of zombies", then Kelemvor says "Burn this place down." He approves greatly of the approach "get in there and bust some zombie skulls" and thinks that the approach "systematically manipulate the Witchlord of Praewith to draw him to a confrontation outside of his region of power" is needlessly complex and possibly cowardly by comparison.
He is probably pretty similar to the followers he draws:
Members of the clergy tend to be taciturn, even morose at times. Many came to the church after losing loved ones to undead incursions, or even after dying themselves and being so profoundly touched by the experience that they enrolled in the clergy shortly after returning to life.
His doctrines seem to mostly follow finding peace, viewing death as a transition rather than a final ending, treating others with equanimity.
Summary of what we explicitly know
Nowhere does it state that he particularly values candor above all other things. In the "would you lie to Nazis about which way a Jew had run?" he'd probably have your back if you lied to them to spare someone's life from being taken before their time.
However there are strong suggestions that he does not like systematically manipulating other people, views it a waste to trap yourself in a web of lies, and thinks idle talk (gossip, lying) is stupid. In any case it seems like Kelemvor probably doesn't like you, because you're Chaotic Good and he's Lawful Neutral and you're professing to be his devotee but that's not how he rolls. (He'd be cool with you if you just manned up and followed a god who's good with Chaotic Good stuff though.)
Real-life religions and lying
Okay, now in my experience if you can give a GM a good story they can potentially allow you to do better when you're acting highly cross-alignment. So let me give you a couple story-bases that you might lean on, in order to better justify your Chaotic alignment following a Lawful deity.
The further sections of the 3e manual above talk about the heavily ritualized ceremonies of death; Kelemvor likes a ritualistic heads-up from a cleric when someone nearby has died and wants everyone to have a priest to perform those ceremonies when they die. He also has a bigger Lament for the Fallen for mass deaths. We can possibly infer that Kelemvor greatly prizes social rituals as a means of bonding with each other and easing life's transitions and providing structure to our lives. You can therefore imagine perhaps some Confucianism flavor where for example such things as prayers, handshakes, and greetings have a proper form. Such cultures view coming-of-age rituals as similarly important and accept lying in children but expect better of adults. So this might be a way for the campaign to go: "I've still not done the Rite of Confirmation where I have to put aside my misleading ways and pursue a disciplined, monastic life."
Another tantalizing way to direct the story comes from this:
Many of the older members of the clergy once worshiped Myrkul, and even fourteen years after that deity's destruction, some have difficulty coming to grips with the doctrinal differences between the two faiths.
This might give you a better story background to stand on. It is possible that your teachers were former worshipers of Myrkul, who was an intelligent strategist and a great master of irony. Given that Kelemvor does not explicitly speak against lying, they might have taught something like the Mahayana Buddhists' "skillful means" doctrine.
One "skillful means" story, for example, comes from chapter 3 of the Lotus Sutra (paragraph beginning "Let us suppose...") and deals with a time where there were lots of "denominations" of Buddhism, with the Buddha explaining why this was so and why those are good but this "Mahayana" Buddhism is better. I'm going to paraphrase for a modern ear:
A father comes home and finds out that his house is on fire, and his sons are upstairs, unaware. "Guys you have to come out, the house is on fire!" he yells, but they can't smell the smoke so they yell back "Haha, very funny Dad. We're having fun playing our racing videogames up here, you should join us!"... So he yells back up there, "Okay, you got me, I have an agenda! Put down those racing games, 'cause do you remember yesterday when we were talking about cars? Mark, you wanted a Porsche, well I bought you this beautiful Porche 911, and Matt you said that you didn't like Porsche but you wanted a BMW, well I went out and bought you a shiny BMW Z4..." and with that, his sons come running out excited to see their new cars. But there's neither BMWs or Porches awaiting them: but the Dad instead gives them his one-of-a-kind knock-your-socks-off amazing car which words can't even begin to describe.
The point is, did the Dad "lie" to his sons? This particular branch of this particular religion says: "no." He (a) did what needed to be done to get the kids out of the dangerous situation, and (b) ultimately gave them what they really wanted, but "down-sold" it to make it easier to explain to them. He therefore wasn't being "deceitful" so much as "skillful." So, maybe your teachers were former Myrkul-worshippers who value a certain "skillfulness" in achieving the greater means of the priesthood, and perhaps Kelemvor tolerates this sort of lying if it generates results and doesn't get out of hand.
Another great real-life source that seems to gel with Kelemvor's equanimity and morose followers might be the Biblical book of Ecclesiastes, which essentially says "Enjoy the good things while you got them -- you aren't gonna have them long, but of course that's OK too. Striving of course is pointless but then again you can't really help it because striving to strive-for-nothing is its own sort of striving, so you might as well strive for good things and wisdom. But above all things just pursue a balanced life." The Ecclesiaster says for example "Do not be too righteous, and do not act too wise; why should you destroy yourself? Do not be too wicked, and do not be a fool; why should you die before your time?"
Along those lines, it's possible that Kelemvor, while he himself lives a very orderly life, doesn't see the point in being all holier-than-thou about lying towards his followers. Maybe the very obsession with "you're misleading people too much" is perceived by him to be a waste of his time: "if you get caught in a web of lies and everyone hates you, well, that's your business, not mine. I'm not going to say you're False just because you did something stupid." If that's his attitude, then maybe there's more room for leeway for a Chaotic follower.
