Allow users to download your own paid app for free in Android

You can now generate and distribute promo codes to current and new users on Google Play to drive engagement. Under the Promotions tab in the Developer Console, you can set up promo codes for your apps, games, and in-app products to distribute in your own marketing campaigns (up to 500 codes per app, per quarter). Consider using promo codes to reward loyal users and attract new customers.

Reference: 1) http://android-developers.blogspot.in/2016/01/create-promo-codes-for-your-apps-and-in.html

2) https://support.google.com/googleplay/android-developer/answer/6321495

The best solution is to have them buy the app, then refund their purchase. It would still show up as paid. Alternatively, you could give them the app, and license it via the LVL, and configure their email addresses as test accounts listing as purchased., but then they won't get updates.