I did that after ending no 2, which I tried doing that route but didnt get invited.
The invitation ending gives you the instructions to get the 3rd ending, it tells you to turn off the power while playing Hide n' Seek with Lily. You trigger the new content by touching the chair (beating Lily in HnS) WHILE the power is out. This can be done in a already finished game, by "Repearing" Lily. The Repear button is there not only to fix errors in the assignments, but also as a replay function. It mostly serves the purpouse of not having to replay the entire game to get different endings, as that would get way too repetitive. You don't need to get the first 2 endings to get the 3rd and 4th, it just tells you HOW to get them.
1st Ending - Finish the game regularly, make at least one mistake
2nd Ending - Finish the game regularly, have no mistakes
3rd Ending - Beat Lily HnS while the power is out, interact with the Craftsman
4th Ending - Beat Lily HnS while the power is out, let go of Susie (won't spoil how, but it is pretty simple), interact with the Craftsman
Hope this helps you out!