After talking to our Support lead, The database connection settings take precedence over the Lock allowSignUp attribute.
If the database connection is set to disable signups, setting allowSignUp: true in Lock will not override this setting and therefore will not show the sign up tab. In the Lock Configuration Docs it states: “Keep in mind that if the database connection has sign ups disabled or you are using a custom database which doesn’t have a create script, then the sign up screen won’t be available.”
Further, the signUpLink parameter will only work when, allowSignUp: true and the database connection is set to enable sign ups. If you would like to change this, Lock is open source and you could possibly update the library to work for your scenario.
Please let me know if this helps answer your question. Thanks!