When nslookup prints Non-authoritative answer: before a result, it is telling you something specific about where that answer came from.
Two kinds of server
DNS has authoritative servers and recursive resolvers. An authoritative server holds the actual zone data for a domain; it is the source of truth. A recursive resolver (like 1.1.1.1 or 8.8.8.8, or your ISP's) does not own any zones. It answers on your behalf by asking the authoritative servers and then caching the result for its TTL.
When you query a recursive resolver and it answers from that cache, the answer is non-authoritative: correct, but a copy, possibly a few seconds or minutes old. That is what the marker means. When the marker is absent, you reached a server that is authoritative for the name, and the data came straight from the zone.
Why non-authoritative is usually fine
For everyday lookups, a non-authoritative answer is exactly what you want: it is fast, and the TTL keeps it fresh enough. Caching is the whole reason DNS scales. You only care about the distinction when the cache might be stale, which is precisely when you have just changed a record and are waiting for the world to catch up.
Getting an authoritative answer
If you need the current truth, bypass the cache and ask an authoritative server directly. Find the zone's name servers (an NS lookup), then query one of them: in nslookup, run server ns1.example.com. and then the name; in dig, use dig @ns1.example.com example.com. The answer will come back without the non-authoritative marker (and in dig, with the aa flag set), telling you that you are looking at the zone itself rather than someone's cached copy of it.