How do I transfer my spring boot app to aws lambda

I have got a pretty basic REST API I have built with spring-boot and I currently have it deployed on AWS EC2. I would like to try out AWS lambda, however, it is still unclear to me what changes I need to make to my code in order for it to run as lambda function. I have looked up tutorials online but none of them have worked so far.

What additions should I make to my files (such as adding LambdaHandler.Java and sam.yml etc.) in order to run this as aws lambda function? Is it relatively easy to make this sort of app run as aws lambda function or should I just stick with ec2?

my project structure is as follows:

|-- product-service
    |-- .idea
    |-- scripts
    |-- src
        |-- main
            |-- java
                |-- com.product
                    |-- controllers
                    |-- domain
                    |-- dto
                    |-- repositories
                    |-- services
                    |-- util
                    |-- Application.java
            |-- resources
        |-- test
    |-- target
    |-- appspec.yml
    |-- buildspec.yml
    |-- product-service.iml
    |-- pom.xml

Application.java looks like this:

package com.product;

import org.springframework.boot.SpringApplication;
import org.springframework.boot.autoconfigure.SpringBootApplication;
import org.springframework.cloud.openfeign.EnableFeignClients;

@SpringBootApplication
@EnableFeignClients
public class Application{

    public static void main(String[] args) {
        SpringApplication.run(Application.class, args);
    }
}

Controller looks like this:

package com.product.controllers;

import com.product.dto.ProductDTO;
import com.product.dto.ProductListDTO;
import com.product.services.ProductService;
import org.springframework.beans.factory.annotation.Autowired;
import org.springframework.web.bind.annotation.*;
import java.util.List;

@RestController
class ProductController {

    @Autowired
    ProductService productService;

    @RequestMapping("/")
    public String getHomePage() {
        return "Welcome to the home page!";
    }

    @RequestMapping("/products")
    public List<ProductListDTO> getAllProducts() {
        return productService.getAllProducts();
    }

    @RequestMapping("/products/{id}")
    public ProductDTO getProductById(@PathVariable("id") String id) {
        return productService.getProductById(id);
    }
}

This then gets built into jar file using -mvn clean install

You need to refactor (rewrite a bit) to perform the migrate from Spring Boot application (Rest APIs) to Lambda based.

Couple notes

A.

1. You can approach Single Lambda for multiple APIs
   or
2. You can approach Multiple Lambda for multiple APIs

B. You can replace Spring dependencies by using Dagger (or similar ones)

C. You can migrate your service/dao classses from Spring Boot to Lambda

D. Setup AWS CloudWatch Scheduler to warm Lambda(s) if required.