So, I took a look at the LANKHMAR map, cards, tokens, and rulebook in hopes that this might turn up some Lankhmar lore—details about Leiber & Fischer's world from early after its creation that might not have made it into the fiction. There turns out to be very little of this, though what's there is intriguing (see below). The biggest change is in accepting that the Gray Mouser and Fafhrd are here just two of four co-equal heroes (each being one player's character), the other two being Pulgh of Lankhmar and Movarl of Kvaach Nar. Fafhrd leads a Mingol army while The Mouser fights on behalf of the Chosen of the King of Kings (a figure wholly unknown to me).
Now that I've looked through the rules, I'd say the game play must be fairly chaotic,* since there are multiple elements that disrupt each player's plans. The most amusing of these are the GEAS cards. Each player has to draw one of these at the start of each turn, and they represent quests that either Sheelba or Nignauble force that player to go on. That hero has to either temporarily abandon the war and take on the geas himself or delegate it to one of his minions. Typical Geases include
• "Go to the Trollstep Mountains to learn the trollstep dance and report back to Sheelba"
• "Go to the City of Ghouls and bring back a Ghoul-friend for Ningauble"
and my personal favorite:
• "Find an earthworm from Earth's End and bring it to Sheelba".
Sometimes Sheelba will lend her boat to help out a hero, Sheelba's boat being another new element.
The typical reward for fulfilling a GEAS is to be free of it, but sometimes there's a Reward, with effects detailed on the REWARD card.
The most interesting of these involve an elusive character known as the War Cat, who appears on two of the cards. The War Cat gives out gifts to heroes, but there's no clue of what he, or she, or It might be, though we do know that it lives in a cave (the Cave of the War Cat) on the far west of the map.*
1st card. "Go to the Cave of the War Cat and gain your choice of a sword, spear, axe, or bow and arrow"
2nd card. "The War Cat gives you aid in combat: Add +1 to the die roll of the man of your choice (hold until used). Discard when used."
So, who or what is the War Cat? In the absence of any other evidence I'd have assumed something along the lines of the Cath Paluc. But in the game it functions as a sort of minor Sheelba/Ningauble --less perilous to approach, distributing lesser reward. The parallel between the names Gray Mouser and War Cat makes me think the Cat is a who, not a what. That visitors are given weapons suggests faint echoes of Scathach, but that's probably pushing it.
Unless of course it's just something Gygax or one of the other mid-seventies re-casters of the game put it in as some kind of private joke.
Perhaps someday we'll get a book-length study of Leiber that'll answer questions like these.
*one good example of this is the Sunken Lands, a land-bridge that submerges at unpredictable intervals, possibly drowning an army crossing the land-bridge at the time.