... And the spectators cannot enter and walk through the path next to the rink to go to the bathrooms etc, I guess?
Happy to say that multiple restrooms are conveniently located within 1980 Rink/Herb Brooks; plus additional restroom options are nearby within Lake Placid Olympic Center.
If you are on "concourse" (for lack of a better word) level inside Herb Brooks (I mean right behind the top row of red seats), restrooms are located in all four corners, IIRC.
If you are on "concourse" level and exit the rink to grab some food a few feet away at Roamers Cafe (on the same level), you will be very near to other restrooms, sort of behind the glass elevator, IIRC. I think you have to go down half a flight of stairs to get to the restrooms (I believe the elevator also stops on restroom level).
If you walk down (or take the elevator down) to ground level, it has restrooms too -- near the information desk/Olympic Museum/Miracle Moments Store, all of which are right next to each other within Olympic Center.
Back up by Roamers, if you walk past Roamers seating area and then down the hall (in opposite direction from 1980 Rink), Olympic Center also has restrooms on the far side of 1932 Rink/Jack Shea Arena (I do not mean within 1932 Rink). (BTW, it seems possible to me that 1932 Rink would have some unofficial practice ice for 2025 Skate America -- as it did for 2017 Skate America, at least on Wednesday, as I discovered by accident back then.)
(Sorry if my explanation of where things are is confusing. There is more than one way to enter 1980 Rink. My examples of restrooms are not an exhaustive list. I'm just trying to convey that walking on the path down by the boards is not necessary at all for easy access to restrooms.

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ETA:
Found a 1980 Rink map for 2023 Synchro Worlds. What I was saying about all four corners is that restrooms are somewhere behind/near top rows of Sections 24/25 and 15/16. Also 3 and 11, I think, although that side is not familiar to me.
One of the ways to enter/exit 1980 Rink is through doors behind top rows of Sections 1/26. Just outside these doors is Roamers Cafe; also the glass elevator.
ETA:
Roamers Cafe is something new since 2017 Skate America. It has lovely mountain views. It was part of the Olympic Center upgrading before 2023 University Games, IIRC. The old cafeteria (as I think it was called) is long gone.