I don’t think you understand what locking does. It locks (forgets the key to) the local database. That’s all.
2FA is only usable against a remote service (or it is useless).
If you want to use your 2FA token (which ever it is) to unlock your local database it means that you need somehow to be able retrieve the key from somewhere safe locally.
“Fingerprint unlocking” is somewhat safe on a trusted platform like Android or iOS because the secret is made hard to extract by hardware & OS-level security measures, but in a browser on a PC that just impossible to do well. @kspearrin please correct me if I’m wrong…
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