I would use mud on the threshold inside and top. You want no nails through
the membrane. I wrapped the lath over the top and down about 1" on the
outside of the shower, so that it would hold itself in place over the
membrane.
I nailed backerboard below that to help guide the trowel for shaping the
mud.

I did see a pro who glued some kind of backerboard (siliconized gypsum?)
to glued down membrane over the threshold. I believe he clamped backerboard
to the threshold to press the membrane into its glue to attach it, with
weights on
the top. He used special glue for this.

Bob

Thanks Bob! This seemed like a logical thing to do, so I did exactly
that last night, except I didn't wrap the lath over and down, on the
outside. I mudded the floor, which seems to have held the lath in
place, just fine. Tonight, I will mud the threshold, and get ready to
move on to tile! ;-)

I'm sure I'll be back soon, with some tile questions!

Best Regards,
Todd