Nikko pass

Good morning,
I need your assistance to understand if I need to buy Nikko pass for 2 days or World heritsge pass.
On one hand I will be in Nikko 2 days, on the other hand I would like to visit on the 2nd day Lake Chūzenji and Kegon Falls.

Thank you in advance,
Anna

You never NEED do buy any passes. But passes can provide a discount over regular tickets depending on your itinerary. If you visit Nikko and Lake Chuzenjiko/ Kegon Falls, then a

Nikko World Heritage Area Pass = 2,120 yen plus the bus fare to Kegon Falls (which I think would be 2200 yen; or a Chuzenji Onsen Free Pass for 2300 yen for free bus travel between Nikko and Chuzenjiko)

Or the Nikko All Area Pass covers everything (and more) for 4,780 yen (4,160 yen in winter).

The 2300 Pass for 2 days covers the lake and kegon falls and is cheaper than the return bus trip (2500)

It is possible to see both Kegon Falls and Lake Chuzenji in a day. The falls are actually quite impressive.
https://youtu.be/17Tza6USdYM

But you really need to carry a schedule of the buses with you, because they are not that frequent and if you don't, you could end up waiting over an hour for a bus. Not to mention, knowing the last bus back is also important. There are several sights around the lake, so you should figure out how you are going to spend your time and get around there also. Some places are not far, but others like Ryuzu Falls are more out there.

In addition to the comment @Ken made about buses, if going on a busy day (weekend in autumn for example), the traffic and buses are crowded and the wait times can be very long. No guarantee you'll get on the first bus.
Outside of that, I have found the bus service to be quite good, and the 2-day pass good value for money.

If you visit all of Kegon Fall, Chuzenji Lake and Toshogu Shrine, then, you should have Chuzenji Onsen Free Pass, which is 2,300 YEN (unlimited use for 2 days).
If you visit even Yutaki Fall (highly recommendable), Senjogahara Moor, Ryuzu Fall as well as above sites, then, Yumoto Onsen Free Pass, which is 3,500 YEN is the best option (unlimited use for two days).
World Heritage Pass is only recommendable who visit Toshogu Shrine and Rinnoji Temple area only.

FYI, so far, you can visit both Kegon Fall and Toshogu by one day trip from Tokyo. However, please estimate extra time for traffic jam between October and November.