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I have worked on a similar scenario; running Nuxt in a lambda behind CloudFront. For that scenario you need to connect your nuxt lambda with API Gateway, then add the API Gateway as an Origin in CloudFront. If you want all requests on domain.com/app to hit Nuxt, you then set a CloudFront behaviour to forward all requests to /app/* to the API Gateway Origin you just added.
So unsure whether you need to front your EC2 with API Gateway, or if you can directly add EC2 as a CloudFront Origin, but look for info on using EC2 as a cloudfront origin and you should be fine.
Source:stackexchange.com