Managing user lookup keys in API does not work?

I am using version 2.9

I have found this article regarding managing user lookups in docs:

Based on that, I should be able to set up user lookup via command like this:

PUT /api/v2/system/user/100?related=user_lookup_by_user_id
“user_lookup_by_user_id”: [{
“name”: “favorite_food”,
“value”: “pizza”,
“private”: false,
“description”: null

I, however get back following error:
Unknown relationship: user_lookup_by_user_id"

Am I doing something wrong or is this a bug?

Many thanks