There is no need to transfer the domain over. You can create an A record from your domain name provider point it to the Public IP of the site hosted in LightSail.
Even though it is recommended that you transfer management of your domain's DNS records to Lightsail. This allows you to efficiently administer your domain and compute resources together in one place . This guide shows you how to create a Lightsail DNS zone for your domain, and how to transfer management of your domain's DNS records to Lightsail. After transferring management of your domain's DNS records to Lightsail, you will continue to manage renewals and billing for your domain at your domain's registrar. The following document  shows you how to to point a domain to an Amazon Lightsail instance using Amazon Route 53 .
References  https://lightsail.aws.amazon.com/ls/docs/en_us/articles/lightsail-how-to-create-dns-entry  https://lightsail.aws.amazon.com/ls/docs/en_us/articles/amazon-lightsail-using-route-53-to-point-a-domain-to-an-instance
I hope the Information above helps. Feel free to reach out for any concerns. Thank you
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