Apex domains cannot have CNAME records.
Question and response
Question
dig lwx.net.nz. NS
Answer
lwx.net.nz. 5 NS ns-1355.awsdns-41.org.
lwx.net.nz. 5 NS ns-111.awsdns-13.com.
lwx.net.nz. 5 NS ns-839.awsdns-40.net.
lwx.net.nz. 5 NS ns-1718.awsdns-22.co.uk.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0