cross origin for amazon lambda function from localhost in gatsby site

I have the following code which works when I run it as a local serverless function with netlify dev, but I need it to run cross origin from a dev server to the hosted server function. I put the function in a aws lambda function but I am getting a cross origin blocked error on my https:dev.website.com, I thought I have the correct headers in the return object so not sure why I am getting a cross origin error.

Any help would be great

const sanityClient = require("@sanity/client");
const client = sanityClient({
  projectId: "random-id",
  dataset: "production",
  useCdn: true,
});

exports.lambdaHandler = async (event, context) => {
  var body = JSON.parse(event.body);

  //console.log(body.price_id)

  try {
    const checkPriceId = async (test) => {
      const query = `*[_type == "products" && price_id == "${body.price_id}"]`;

      const documents = await client.fetch(query, {}); // this could throw

      return documents.map((document) => document.sold);
    };

    var ok = checkPriceId().then((test) => {
      return new Promise(function (resolve, reject) {
        //console.log(test) // this will log the return value from line 7
        console.log(test);
        resolve(test);
      });
    });

    var bools = await ok;
    // prettier-ignore

    return {
      statusCode: 200,
      headers: {
        'Access-Control-Allow-Origin': '*',
        'Access-Control-Allow-Headers': 'Content-Type',
        'Access-Control-Allow-Methods':'GET, POST, OPTION',
      },
      body: JSON.stringify({
        sold: bools,
      }),
    };
  } catch (err) {
    return { statusCode: 500, body: err.toString() };
  }
};

This is my request to the function if that helps

 var fetchUrl = https://random.executue-api.aws.com/prod/sold //not exact 

 var fetchData = async function () {
    const response = await fetch(fetchUrl, {
      method: "post",
      headers: {
        "Content-Type": "application/json",
      },
      body: JSON.stringify({
        price_id: final,
      }),
    })
      .then(res => {
        return res.json()
      })
      .catch(error => console.log(error))

    return response
  }

Update:

I tried adding cors the way suggested in the answer below, but it failed seen below so I tried manually adding the method response seen after.

I still get a cross domain error. And I have changed the domain so it is now https as well. Really stuck here.

I was looking into this more, and it seems like before it does the actual post it does a cors check at the options method, so I added in the same access control headers, and deployed but did not work. Don't quite get this.

from cross origin for amazon lambda function from localhost in gatsby site