Using Lightsail with Cloudfront

I've previously used Cloudfront with S3 and also with WordPress sites hosted on Lightsail. I'm now trying to set up a Cloudfront distribution for standard websites (non WordPress) hosted on Lightsail, (without a Load Balancer). I note that the Cloudfront distribution seems to hit the 'default' Lightsail page (This can be the Plesk default page if you're using Plesk or the default website - if you have set one as default). There doesn't seem to be any way of targeting a second or third site hosted on the Lightsail instance with a Cloudfront distribution. Does this mean I can only have one Cloudfront distribution for a single site on a Lightsail instance or has anyone come across a workaround?