Hello,
with the site lock function, the custom registration form does not work.
it uses the BuddyPress default registration and sends the activation email.
user has to activate the account only then they will be able to log in.
note: the general idea behind this scenario was to prevent the spams, like bot or users with dummy email could not sign in to your BuddyPress site.
in the meanwhile you could try third party plugin to . achieve this:
https://wordpress.org/plugins/auto-login-new-user-after-registration/
please let me know.