Warren was attempting to evoke a reaction from Bob to confirm his suspicion that Bob was lying.
The film establishes Warren as someone who regularly lies and fabricates stories, e.g., the Lincoln Letter, to get other people to act, or react in a way favorable to him. It's in character for him to make up the story about the sign.
Warren had been doubting Bob's story and had been suspecting Bob of foul play. Ever since Warren arrived at Minnie's Haberdashery, he had noticed that something was off: Bob's story of Minnie visiting her mother and being gone for a week ("Minnie never struck me as the sentimental type"), Sweet Dave leaving his chair ("I can't imagine
Sweet Dave lifting his fat ass out his chair long enough to fetch well water..."), Bob not enforcing Minnie's "no hats indoors" policy ("kind of rule she'd want kept up in her absence"), the jellybean between the floorboards, and the jellybean jar being missing from the shelf (suggesting some kind of scruffle took place).
In addition to the signs of foul play above, prior to the "no dogs or Mexicans" sign conversation, Warren had established that the stew was made by Minnie and not Bob based on its taste ("So if Minnie is on the north side visitin' her mama for a week, how'd she make the stew this mornin'?"), and had seen Sweet Dave's blood on the chair.
At the point of the "no dogs or Mexicans" sign conversation, Warren was attempting to evoke a reaction from Bob to confirm his suspicion that Bob was lying. ("And if you lyin', which you are... Then you killed Minnie. And Sweet Dave.")
Bob: You're a real imaginative n*r, ain't you?
Bob: So, do you intend to murder me based on a far-fetched n*r theory, or can you prove it, cabron?
Warren: It ain't so far-fetched, Señor Bob. And it's a little bit more
than a theory.
Warren: How long you say you been workin' for Minnie?
Bob: Four months.
Bob reacted to the "no dogs or Mexicans" sign story in a way that gives the impression that he was not familiar enough with Minnie to confirm or deny it. Had he actually been working for Minnie for four months as he claimed, he would have had a different reaction to the story and be able to call Warren's bluff. Since Bob just met Minnie earlier that day, he didn't (and couldn't) call Warren's bluff. Based on Bob's reaction to the story, Warren was sure enough that Bob was lying and that Bob is actually working with Daisy Domergue.
What Warren did is similar to what he tried to do in an earlier conversation with Bob:
Warren: She still stinking up the place with Old Quail pipe tobacco?
Bob: Minnie doesn't smoke a pipe. She rolls her own. Red Apple Tobacco.
Bob: But, mi n*o amigo, I think you already know this.
Warren: Yeah, I do, Señor Bob. Just seeing if you do.
Here, Warren lied to try to figure out if Bob was familiar with Minnie. Bob was able to give a satisfactory reply at that time since he was in the haberdashery when Minnie mentioned (to Jody) that she smokes Red Apple Tobacco.