See finished script: https://github.com/xdmorgan/netlify-functions/blob/master/functions/mailchimp-subscribe/README.md

mailchimp.js

const Mailchimp = require("mailchimp-api-v3");
const validate = require("./validations");

const { MAILCHIMP_API_KEY } = process.env;

exports.handler = async (event, context) => {
  // require an API key or throw everytime
  const [is_valid_env, invalid_env_response] = check_env(process.env);
  if (!is_valid_env) return invalid_env_response;
  // 0. validate request body
  const [body, is_valid_body, invalid_body_response] = check_body(event.body);
  // 0b. Return 400 - Bad request
  if (!is_valid_body) return invalid_body_response;
  // 0a. Continue;
  const { email, list_id, interests = [] } = body;
  // 1. Create API instance
  const mc_api = new Mailchimp(MAILCHIMP_API_KEY);
  // 2. Already a member?
  const check_opts = { email, list_id };
  const [is_member, is_subscribed, exists_response] = await check_member_exists(
    check_opts,
    mc_api
  );
  // 2a. If they are, are they subscribed status?
  // 2aa. Great! DONE 200
  if (is_member && is_subscribed) return exists_response;
  // 2ab. PUT to update status as 'subscribed'. DONE 200
  if (is_member && !is_subscribed) {
    const update_opts = { email, list_id, status: "subscribed", interests };
    const [updated_response] = await update_member(update_opts, mc_api);
    return updated_response;
  }
  // 2b. If they're not, continue;
  // 3. Create list member
  const create_opts = { email, list_id, interests };
  const [created, create_succeeded, create_failed] = await create_member(
    create_opts,
    mc_api
  );
  // 3a. If succeeds, DONE 200
  return created ? create_succeeded : create_failed;
  // 3b. If fails, return 500
};

function check_env({ MAILCHIMP_API_KEY } = {}) {
  const is_valid = !!MAILCHIMP_API_KEY;
  const response = { statusCode: 500, message: "missing env vars" };
  return [is_valid, response];
}

function check_body(request_body) {
  const body = JSON.parse(request_body);
  const is_valid = true; // check email, check list_id
  const response = { statusCode: 400, message: "invalid request" };
  return [body, is_valid, response];
}

async function check_member_exists({ email, list_id }, api) {
  const is_member = true;
  const is_subscribed = false;
  const response = { statusCode: 200, message: "already subscribed" };
  return [is_member, is_subscribed, response];
}

async function update_member({ email, list_id, status, interests }, api) {
  const request = create_request_body({ email, list_id, status, interests });
  const response = { statusCode: 200, message: "subscription updated" };
  return [response];
}

async function create_member({ email, list_id, status, interests }, api) {
  const request = create_request_body({ email, list_id, status, interests });
  const success_response = { statusCode: 200, message: "create succeeded" };
  const error_response = { statusCode: 500, message: "create failed" };
  return [success_response, error_response];
}

function create_request_body({
  email = "",
  interests = [],
  status = "subscribed",
  merge_fields = {}
} = {}) {
  return {
    email_address: email,
    status,
    merge_fields,
    interests: interests.reduce((acc, cur) => ({ ...acc, [cur]: true }), {})
  };
}

The general approach. For the implementation, see my Netlify functions repo: https://github.com/xdmorgan/netlify-functions/blob/master/functions/mailchimp-subscribe/README.md