How can I force to display different tab on Lock widget in the universal login page with Android?

You could pass custom parameters to the universal page with withParameters attribute in the Android SDK. Once this is implemented like below, you should be able to get the requested value in the config.extraParams.mode in the hosted login page.

    Map<String, Object> parameters = Collections.singletonMap("mode", (Object) "signUp");
    WebAuthProvider.init(account)
            .withParameters(parameters)
            .start(activity, callback);

Then you could use the passed custom parameter to change the initialScreen attribute. This QA can be useful for the last part while configuring the hosted login page.

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