TypeScript functions on Firebase - paths problem

My Firebase project has TypeScript functions implemented with the following directory hierarchy:

- functions
  - src
    - index.ts
  - shared
    - other.ts
  - tsconfig.json
  - package.json

My tsconfig.json file looks like:

{
  "compilerOptions": {
    "module": "commonjs",
    "noImplicitReturns": true,
    "noUnusedLocals": true,
    "outDir": "lib",
    "sourceMap": true,
    "strict": true,
    "target": "es2017",
    "resolveJsonModule": true
  },
  "compileOnSave": true,
  "include": [
    "src"
  ]
}

And my package.json:

{
  "name": "functions",
  "scripts": {
    "lint": "eslint --ext .js,.ts .",
    "build": "tsc -b",
    "serve": "npm run build && firebase emulators:start --only functions",
    "shell": "npm run build && firebase functions:shell",
    "start": "npm run shell",
    "deploy": "firebase deploy --only functions",
    "logs": "firebase functions:log",
    "test": "mocha --reporter spec 'test/**/*.ts'" 
  },
  "engines": {
    "node": "12"
  },
  "main": "lib/index.js",
  "dependencies": {
     "dep": "^1.0.0"
  }
}

I'm able to compile the project with npm run build (which translates to tsc -b), but can't serve (firebase emulators:start) due to the following error:

Error: Cannot find module './functions/lib/index.js'. Please verify that the package.json has a valid "main" entry

To my surprise, the lib folder contains two new src & shared folders instead of the "compiled" JS directly under it. How can I fix it?