Sonny writes:
From what you have described, plaster and lathe, I wouldn't think the
plaster and lathe is along the bottom of the stair stringers, but
encases some cavity under the stairs. Since you will open that area,
why not finish the interior, there, for storage or other and create an
access door, concealed, maybe, if an obvious door would not complement
the surounding design/decor/trim.

If there is such an area, accessing a tread should not be an issue, in
order to secure the tread easily.

Actually, the area under the stairs is now open with the plaster & lathe
underside of the stairs closely following the rise of the stairs.

I have often thought about enclosing the underside to add storage but
the stairs are parallel to a narrow hallway and I am concerned that
closing off the underside may make the space feel more constricted. Not
sure though and will likely consult an architect at some point or draw
it all in sketchup