Hello @msagweb, welcome! 
Let’s Encrypt offers Domain Validation (DV) certificates.
Thus you need to own and have control over the Domain Name (or have a subdomain under an existing domain name, for example pointed to your server by your employer or school) you wish to obtain a certificate for, from an ICANN Accredited Registrar.
In the title you state non-public domain, Let's Encrypt does not offer certificates of that type.
Here is a link Create Local SSL