Apex domains cannot have CNAME records.
Question and response
Question
dig lsusp.com. NS
Answer
lsusp.com. 4 NS lsu-bdds4.lsu.edu.
lsusp.com. 4 NS lsu-bdds2.lsu.edu.
Authority
The response has no authority records.
Additional
lsu-bdds2.lsu.edu. 4 A 192.16.176.89
lsu-bdds4.lsu.edu. 4 A 192.16.176.87
lsu-bdds2.lsu.edu. 4 AAAA 2620:105:b050:1550:0:0:0:89
lsu-bdds4.lsu.edu. 4 AAAA 2620:105:b050:1550:0:0:0:87
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0