It's just informal English. If he/she wanted to write it in a formal way, they would say "no one ever needs to know" :)

I don't think this sentence is wrong, I think "no one" is singular in regular way, but when the autor think there should have some people participate but the result is nobody, in this condition, no one should be plural. For example, I thought there should be a lot of guys to attend this activity, but no one came. This "no one" should be plural I think~~

"No-one ever need know." - this is perfectly correct, but often used as a stock phrase in English. Technically, "need" functions here as a modal and a subjunctive phrase is created (this doesn't happen often, but please pay attention when it does). To me, this sounds more formal. The average English speaker will accept this as perfectly fine without needing to think about it too much. "No-one ever needs to know." - This is the standard grammar for indicative mood: you're stating a reality. In this case, both phrases are interchangeable but the indicative phrase ("...needs to know") sounds a little simplistic.