From what I know is that you can peer the Lightsail (AWS-managed) VPC with your normal, default EC2 VPC via the Lightsail console. Then you launch EC2 instances in the default VPC for the transfer
Fun fact is, that Netflix only hosts their website on AWS, the video stream is delivered from their very own CDN which is completely self-engineered by them and multiple magnitudes cheaper than AWS: https://openconnect.netflix.com/
Interesting, I like the fact that "Replicated objects can be owned by the same AWS account as the original copy or by different accounts, to protect from accidental deletion." is something they thought of.