Hi there,
Skip the embedded forms, this is Webflow 
Instead, use a native Webflow form and send the submission into Make (Integromat):
Then add a MailerLite module:
When you submit the Webflow form, whatever the user added will show up here. Basically, ask them for an email address and it’ll be here for you.
Create a new subscriber:
I don’t use MailerLite but I’m assuming this will work for you.
And then the secret magic is to add this as the last module:
You can redirect the browser anywhere you want after the form submission.
Or if you want to make it fancy, there is some Javascript you can copy / paste in my screencast walking throug this setup (minus MailerLite):
Hope that helps!