Apex domains cannot have CNAME records.
Question and response
Question
dig lu. NS
Answer
lu. 3 NS j.dns.lu.
lu. 3 NS k.dns.lu.
lu. 3 NS g.dns.lu.
lu. 3 NS ns1.dns.lu.
lu. 3 NS p.dns.lu.
lu. 3 NS i.dns.lu.
Authority
The response has no authority records.
Additional
g.dns.lu. 135237 A 194.0.23.5
i.dns.lu. 52334 A 194.146.106.66
j.dns.lu. 135237 A 77.72.229.247
k.dns.lu. 171630 A 194.0.1.13
p.dns.lu. 135237 A 194.0.42.42
ns1.dns.lu. 165186 A 158.64.229.18
g.dns.lu. 135237 AAAA 2001:678:1b:5:0:0:0:5
i.dns.lu. 52334 AAAA 2001:67c:1010:16:0:0:0:53
j.dns.lu. 135237 AAAA 2a01:3f0:0:307:0:0:0:53
k.dns.lu. 171630 AAAA 2001:678:4:0:0:0:0:d
p.dns.lu. 135237 AAAA 2001:678:60:0:0:0:42:42
ns1.dns.lu. 165186 AAAA 2001:a18:4:1:0:0:0:18
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0