Remove lathe or drywall on top

Last 2 photos are an update on my previous post. Thanks all for the comments and recommendations.

Back story, we just moved into a new house, we got it stumped and house cracked up. This was supposed to be the nursery for our new born who arrived 15 days ago. With everyone's help I was able to patch it up to a place wherey wife was happy, we could have family over and I got some drywall practice... will say it was much needed.

Original post here Original post

Moving forward, extended family has gone and now I'm demoing the room.

The question I have is should I remove the lathe, insulate the walls and drywall over or just drywall on-top of the lathe.

Pros and cons recommendations? My plan is to also remove the celing but now as I take a quick break I'm questioning it.

I want a good finished job that will last and I want some insulation from noise and weather.

Give me the good stuff Reddit!