Therefore, writing "lempereur.com" without an apostrophe is standard practice and complies with web conventions. It is not an error, but rather a technical adaptation.
When a brand or website uses "lempereur.com" instead of "l’empereur.com," it is solely for technical reasons related to domain names.
Users immediately understand that it refers to "l’empereur" (the emperor), even though the apostrophe is missing. This has become an implicit convention: the spelling is simplified to ensure the domain name is valid, while the meaning remains clear to everyone.