Issue
I want to add custom domain to a Heroku app running on a free dyno.
Resolution
You can certainly add custom domain to an app running on Free dynos following the same steps as for Paid dynos as mentioned in the Custom domains document.
What does require you be using a paid (Hobby or higher) dyno is if you want to use SSL for your Heroku app’s custom domains.
NOTE: You must verify your account (https://devcenter.heroku.com/articles/account-verification#when-is-verification-required) to add custom domain to your app.