I believe you can find her along with some other powerful companions after day 100

Ah, day 100. Thank you very much. I always wondered why some companions took time to spawn. So it's based on days, then. Very nice.

Yeah when the message that said something about song spies appeared, that's when they spawn

ooh I've never heard of Li Shishi. Now I'm intrigued. I found a companion I'd never seen before called Xiao Jiasui in a Shu city around day 140. He's as OP as the hero lords, even stronger than Luan Tingyu [Iron Staff]. He's more of an Infantry and throwing specialist, with an S class in Infantry leadership plus he's a Level 4 Artisan and Level 3 Titan, so he's worth looking for.

I just checked and Li Shishi comes up if you ask a tavern keeper about companions. I'm at day 144, so it fits if they become available after day 100

There's another one called wen huanzhang, really good advisor with S rank leadership in archery and calvary and he also joins you for free