In migrating several domains to AWS via Route53 and setting up a few application instances via AWS Lightsail I discovered that to make things turnkey, AWS sets up a different set of name servers for Lightsail instances so DNS name server entries need to point to Lightsail, not Route53 name servers.
My particular hosting need for a Lightsail hosted instance had mail hosted by Google so here is a quick rundown of how your Lightsail specific MX records should look when pointing to Google.
Remember that in order for Lightsail to properly utilize these records your domain name needs to be pointed at the Lightsail name servers which can be found by logging into AWS Lightsail console and clicking Networking. Here you will find your Global DNS Zones for your hosted application instances. Select your specific domain from the list
Then you will see an option to “+ Add record” which is where you can add your specific MX record entry to route mail. Note you can still map to a domain name not strictly an IP address.
Note: You should confirm your specific MX Record settings in your Gmail admin console