Let’s Encrypt offers Domain Validation (DV) certificates., you have no Domain.
Domain names for issued certificates are all made public in Certificate Transparency logs (e.g. crt.sh | example.com), so withholding your domain name here does not increase secrecy, but only makes it harder for us to provide help.
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.
For Let’s Encrypt to issue a Domain Validation (DV) certificate Domain Validation must happen
and it is a CA/Browser Forum Baseline Requirement.
Let's Encrypt uses Multi-Perspective Validation Improves Domain Validation Security - Let's Encrypt
Since these are Domain Validation (DV) certificates the Domain Name System (DNS) is used extensively in the validation process as well a allowing us to assist here on Let's Encrypt community.
DNS Queries need to give consistent results from any location on the Internet, all your authoritative DNS Servers for the Domain need to also give consistent results as well.