aws-serverless-fastify

app.js

const fastify = require('fastify');

function init(serverFactory) {
  const app = fastify({ serverFactory });
  app.get('/', (request, reply) => reply.send({ hello: 'world' }));
  return app;
}

if (require.main === module) {
  // called directly i.e. "node app"
  init().listen(3000, (err) => {
    if (err) console.error(err);
    console.log('server listening on 3000');
  });
} else {
  // required as a module => executed on aws lambda
  module.exports = init;
}

lambda.js

const awsServerlessExpress = require('aws-serverless-express');
const fastify = require('./app');
let server;
const serverFactory = (handler) => {
  server = awsServerlessExpress.createServer(handler);
  return server;
}
const app = fastify(serverFactory);
exports.handler = (event, context, callback) => {
  context.callbackWaitsForEmptyEventLoop = false;
  app.ready((e) => {
    if (e) return console.error(e.stack || e);
    awsServerlessExpress.proxy(server, event, context, 'CALLBACK', callback);
  });
};

example with claudia.js https://github.com/claudiajs/example-projects/tree/master/fastify-app-lambda

https://www.fastify.io/docs/master/Serverless/