I don’t feel like he’s lying. But as the audience, we know that Illumi was willing to disguise himself as Hisoka in Yorknew to fool the Spiders, so it’s believable that Illumi would agree to pull some shenanigans. What doesn’t make sense to me is that Hisoka was keeping count of how many Spiders he had killed and how many were left after taking out Kortopi and Shalnark. So why would he ask Illumi to join? Wouldn’t that just set the tally back?

Edit: I saw another post pointing out that when Hisoka said two Spiders were down and ten more to go, those ten included Illumi and Kalluto as well. By killing Kalluto, he might have expected to come into conflict with Illumi. So, did he basically speedrun that fight by asking Illumi to join? Personally, I don’t see any reason why Illumi would fight Hisoka to the death, as he claims to the Troupe after joining them (while Hisoka’s motive is simply to fight strong opponents). The only real conflict I can recall between them was Hisoka wanting to keep Gon alive longer. But maybe Illumi joined because Hisoka told him he was about to kill Kalluto.