p.dns.lu has no CNAME records.
Question and response
Question
dig p.dns.lu. NS
Answer
The response has no answer records.
Authority
dns.lu. 1705 SOA ns1.dns.lu. hostmaster.restena.lu. 1772119985 3600 300 2592000 7200
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0