Thanks Alphavictim.
Well - Lita was there with her best friend Toni, and the hotel was called Broadway Plaza. Might not be in the text of the article that I cited, but that's just some additional information...

The whole story is that Lita was making out with Jon when he felt sick. Then she moved to the bed where Richie and Toni were fooling around, before Jon came back. All this in the Broadway Plaza.

Let me re-write the lyrics then:

We go down to the Broadway
[...]
Well I saw Lita (Lita's middle name is Rosanna btw) on the table
Toni down below
They'll give it to the king of swing
Before it's time to go