The guide also only mentions the path if they get caught by nick. It describes the alternative immediate choice but continues only the "caught" path with day 34. But what I can see the guide also mentions that:
That was some time ago and the guide itself admittedly doesn't try to cover every path.
I'm not sure I remember everything right, but reading guide, I think there was a path where Nick did not discover them.
Day 33 Thursday
3rd scene – Bathroom with Fred - 50% stamina
first choice
choose 1.
Put it in
second choice
Choose 2. Turn on light and see
Nick does NOT find out through the one way mirror, so he remains clueless. He goes downstairs and continue with his computer. After a while, Lily comes back down the stairs too, pretending nothing happened.
And the game continues like before.
if he does discover them you go through psychology branch but since he get hypnotized he forgets about what he saw and the two branches (where he discovers and not discover) are merged back together
Having said that, the path where he discovers them is much more fun to play.