What I can suggest is that when the user subscribes using the webform in the external website to call a webform you have created in your Sitefinity project and pass the information entered by the user for example in the query string.
Then in the Sitefinity webform you can get the desired information about the subscriber from the query string and create it using the API. Please refer to the following documentation article
for more details about creating subscribers.
After you create the subscriber, you can add it to the desired mailing list using the sample code from the following article
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