Given how tokens are generated/transferred and how Lockdown Mode specifically blocks a good bit of WebKit, functionality, this may be hard to fix.
Still, the intent of Privacy Pass and Lockdown Mode are arguably aligned, or at least its users overlap. If a fix is not possible, I would request that a greater number of tokens be generated at one time to minimize the number of times one would need to disable/reenable Lockdown Mode. Thank you.
"Generate token" button would ideally work while in Lockdown Mode.