I think the more realistic threat model here is presented by ad networks and major websites doing typical types of browser fingerprinting, like canvas, fonts, etc. as well as possibly some of the techniques mentioned in the article here, like webGL, JIT JS, etc.
In that case of a limited number of trusted sites that we focus on ensuring compatibility with, spoofing is easier, because we can pay a lot of attention to ensuring that our "middleman" fixes the errors introduced by spoofed client-to-server communications.
Some technologies like WebGL will simply never work on a spoofed site, of course. But for the very limited number of sites when users lose important functionality, they can just turn off Lockdown mode.
If a Lockdown'd phone habitually patronizes malicious websites, the protection will never be enough anyway. So we shouldn't worry about protecting against being fingerprinted by a very malicious website - Lockdown users must simply avoid these, with or without a fingerprinting vulnerability!