Mash temperature and efficiency 150vs180

This is sort of a multi-part question...
Did some research into this question today, but could not find a relevant answer....
Maybe I am using the incorrect terminology or am missing something so blatantly obvious it would not be answered often.

scenario:
2 AG batches. Both AG batches with equal amount of water and grain(both being the same type.. say standard 2-row).
Mashed for the same period of time. Both being sparged with the same amount of water at the same temperature.

1 batch mashed at 150F
1 batch mashed at 180F

would both batches measure to the same gravity after sparge?

From what I understand.. They would not be the same. The batch mashed at 150F would have a higher gravity due to the mash temperature.
The batch mashed at 180 would see a decrease or non-existent efficiency to due the enzymes being denatured.

But if they were to end up the same.. would that be due to un-converted starch present in the fluid?
If so would a refractometer give a different reading then a hydrometer?

Nope, you had it right the first time. Its only going to give a reading based off sugar. So, at 180F you've gone and killed everything in the grain before it got started. That's why we mash out at 170F. This stops conversion, and "loosens" sugars in the grain.

So a higher gravity would mean you did a good job? Or will the non fermentables contribute to gravity as well?

Would a pound of lactose in a 5 gallon wort change the gravity?

Non fermentables will add to gravity, its still sugar. You'll see that when you have a beer that doesn't ferment out all the way when you mashed warmer for more body. Mash a bit cooler = more alc and dryer. I suppose higher gravity would be good meaning your efficiency is up or good. Your looking for the proper OG with a very fementable mash.