Objects not available under "Related Entity Type" in Lightning email template

To make email-associated objects available under the "Related Entity Type" picklist, review the following to ensure both flags are set:

1. Ensure "Enhanced Email" is enabled

1. Log in to Salesforce with the System Administrator profile
2. Navigate to Setup | Email | Enhanced Email
3. Click Enable

As soon as Enhanced Email is enabled for the Org, users should be able to select any available object for "Related Entity Type" picklist and create email templates in the Lightning experience. Enhanced Email allows email message records to be created across all object types where an email can be associated or related to such as:  Contacts, Leads, Accounts, Opportunities, Cases, Campaigns, and Person Accounts. Events and Tasks can't have emails associated to them and won't be available in the picklist.

2. Ensure "Track/Allow Activities" is enabled on the Custom Object

1. Open the Object Manager
2. Select the Custom Object to review
3. On the Object Details page, verify that "Track Activities" is selected.  If not checked continue with the next steps to edit the object.
4. Select Edit to edit the object
5. Check Allow Activities

For any objects that have been newly created or where "Allow Activities" has been recently enabled, please allow several hours for the change to be reflect in the "Related Entity Type" picklist.