Can I write a book of my D&D game?

As others have noted, you have to avoid names. You can't use their world or some specific monsters (no illithids!). Other monsters, like gnolls and orcs, predate D&D and thus are fair game (so to speak).

I think the rise of LitRPG shows that plenty of people want to read about game-like worlds, at least as long as you put an interesting twist on it. In my my own series (Sword of the Bright Lady, published by Pyr) experience points are tangible objects, like coins that you can collect and trade. This change lets me write about a fantasy world that is like the ones we play in rather than like the ones that usually get described in stories. My characters talk about being a fourth level wizard and my high ranking warriors can jump off of cliffs without dying. Yet it's not a parody or a game; it's a serious epic (albeit with plenty of humor, as to be expected when a Earth-borne mechanical engineer encounters magic for the first time).

The real problem with writing your game as a novel is that the plot that makes for an exciting game rarely makes for an exciting story, and vice versa. In a game, the players derive satisfaction from their own actions; but in a story, the action of the characters exist to satisfy the reader. One notable exception: The TV show The Expanse is derived from an RPG run by its two authors (there are a couple of places in the books where this is obvious). But clearly they've cut and trimmed the campaign to meet their dramatic needs.

It is sad fact of the publishing industry is that they have seen far too many fantasy novels or trilogies based on the author's D&D games. Nothing loses the interest of a pubisher's fantasy line editor faster than the realization this novel is yet another D&D game turned into a novel. In fact, a number of publishers put their disinterest in publishing D&D or other fantasy games translated into works of fiction, in their submission guidelines.

Expect almost instant rejection (unless your writing is so exceptionally brilliant to overcome this handicap). The problem is too many game-relayed novels have been published. The market is saturated and the novelty is gone.

Yep a whole bunch of game-based novels have been published. That's then, this is now. Publishers and readers have mostly lost interest.

However, if you have a game-based storyline is really good, then you can use that as the basis of a novel. The important thing to do is use as the starting point for fantasy fiction. That means reinvent, reconstruct, and redefine the characters representing your other players, other aspects of the lore of the game, but basically really make them your own.

The main trouble with so much of D&D lore is that is too familiar to fantasy readers and game players. Publishers know this all too well.

Yes you can, for example Record of the Lodoss War started as a Japanese DnD campaign that the DM started writing transcripts which became popular and were novelized and later animated.

You only have to avoid using certain copyrighted words, for example the Beholder copyright is owned by Wizards of the Coast (DnD and Magic publishers) so in the Light Novel/Manga/Anime Goblin Slayer they had to call it Giant Eyeball instead even though the monster was clearly a Beholder.

Note that Paizo, the authors of Pathfinder, publish books in their Golarion setting, but they avoid mentioning certain creatures found in the SRD in their fiction; Pathfinder Tales: Prince of Wolves calls a character "devil-blooded" instead of calling him a tiefling. Along the same lines, their miniature line includes what is clearly a mohrg but labels it Murderous Undead. They are a major corporation effectively publishing unbranded D&D fiction; there are probably legal concerns behind avoiding these names in their fiction.

I think this will depend largely on how much of the lore you're really using. Having underground dark elves that are corrupted by their spider goddess? It'll be pretty obvious, even with some name changes, to anyone familiar with D&D. Some things are more common sense, like red dragons breathing fire and blue ones breathing lightning.

However, when you say "lore", my mind immediately turns to the official settings, and that, I believe, is a complete no-go. Even with some name changes, the setting and lore of Faerun, for example, would likely be fairly obvious to a reader. Big-name characters like Strahd, Vecna, and Drizzt would probably be recognizable, as well. Note that the names of gods, too, would fall into this category-- see the replacement for gods' names used by Matthew Mercer in his Tal'dorei book for reference. (Notably, however, this book is designed for DMs to use to build their own campaigns, and I imagine that many of them, like myself, use his titles and the actual names of the gods interchangeably while playing.)

Consult the System Reference Document for whatever version of the game you've played. It contains all of the information that Wizards of the Coast considers free for use in other creative works. If anything, and I do mean anything, including monsters, locations, and spell names, is not listed there, change the name and description.

Game systems cannot be copyrighted or patented.

However, identifying characters of note or settings are out of the bat.

You cannot make reference to any named character or town from published settings, or use the name of the wizards's spells.

There is also the realm of fan fiction. If you are not profiting from your work and it does not subtract from the value of the main work, you are usually safe.

There is one web novel that did exactly this. Metaworld Chronicles (I'm not affiliated to that) - it began even using references to D&D characters but then swapped them out after the author (allegedly) talked to a WoTC representative.

You can always change the names of people and places found in published official media.

I don't know about the legality of it but this has already been done. A bunch of french players and their dungeon master turned their stories into comic books.

In french it's called "Chroniques de la lune noire", aka "Black moon chronicles". It is very famous among french D&D players. You may want to read on that.

As a fun side note their world and characters were so reputed that Gary Gigax himself once played a session with these guys!

It's imperative that you research what all is trademarked.

Write your book as you see fit, then before final editing/publishing, remove trademark/copyrighted terms/names/phrases from your book and replace them with an alternative that is not trademarked.

Otherwise, you would need permission to use each one. This would be the easiest legal way around this.

If you do not want to go a traditional publishing route, you could always publish your writing online as "fan-fiction", which, of course, is not breaking any commercial-use copyright laws - assuming you are not making money directly from your writing. (But I believe you could still have a Patreon or such, receiving "donations" for your work, rather than being paid for your work directly).