Free tool
The registries for .lu, .be and .eu publish no RDAP, so the domain-info tool has nothing to show for them. This tool asks their whois servers directly and shows what they answer: status, registrar, nameservers and DNSSEC, plus the registry's own text. Registrant details are not published by any of the three; use the registry website for those.
What this checks
Most registries publish registration data over RDAP, a JSON service with a standard format; the domain-info tool uses it. DNS-LU, DNS Belgium and EURid do not, and only offer the older whois protocol on port 43, each in its own text format. All three hide the holder's name and contact details and show them only on their own websites, often after a captcha. What port 43 does give is the status, the registrar, the nameservers and whether the domain is signed, which is what you need for a transfer or a DNS problem.
Related tools
Domains and DNS
Register or transfer .lu, .eu, .be, .com and more; the DNS editor, DNSSEC and the records these tools check are in the client area.