This is not supported out of the box, it’s either link or code, not both. I’ve seen this on other websites as well, but it’s currently not supported at Auth0. For this, you would need to roll your very own implementation, maybe by utilizing the Auth0 API, but definitely also not with Lock (but custom UI).
Side note:
Well, there is a code in the magic link as well, but to get it to work in a way that a user can optionally enter it manually in a UI, is not provided with the link mechanism (as is it with code). So, not an option without quite a lot of additional dev effort.
