4E is not a reliable source anymore, 5E and 4E are very different in some points, like this one. In 5E, when they speak about these 2 clans, it is mostly to depict tensions between both of them. It is even a diplomatic move from the Lion clan to ally with the Crab Clan, as they share the hostility against the Unicorn and plan to invade them. We had a long conversation on French forums to understand why they are not friends, as 4E sounded logical, but in the end we found many explanations to that. There are historic points, but also political ones. If you are interested, you can use Google Translate to read it: http://www.fantasyflightgames.fr/sujet/211516-le_crabe_et_ses_relations_diplomatiques Anyways, for FFG Crab and Unicorn are not in great terms overall.

Hello, Lifthrasir and I made a sheet with diplomatic relationships between the Great Clans: https://docs.google.com/spreadsheets/d/1jfZdoO_FBUMY2F4rRy7Z9Pr-ibmUzuMcxiSvONo_m0k/ The second tab is for English version. Note: we do not found sources for the Crane-Phoenix relationship, so it's empty atm. More tools at https://www.nucreum.com/l5r/