Just as a quick check, I would review the profile you're testing with. Be sure they have visibility to all fields on the new task action and they have the ability to create new tasks. 

I noticed that I am having a hard time getting "New Task" to show up in the Lightning Experience. I've made sure the action was added to the page layout.  I also looked under the different areas actions can be on the Lightning Experience (in the top right, under collaborate, etc..), but I can't get New Task to show up.  

Does anyone have any suggestions for avenues for me to explore? My issue has been hard to google.

Thanks.

Action not showing up in Lightning Experience