Did you know that in Lightning on a case, you cannot create a blank email?  All email functionality currently always pulls in the entire case email thread.

Please upvote this idea: https://success.salesforce.com/ideaView?id=0873A000000CUzhQAG

Removing the thread from the email draft is currently not support in Lightning. Here's an article for more information:

https://help.salesforce.com/articleView?id=000267996&language=en_US&type=1