Send Email button is not in the Activity History related list in Classic nor Chatter actions in Lightning

Set access level to 'All email'

1. Navigate to Deliverability from Setup:

In Salesforce Classic: Setup | Administer | Email Administration | Deliverability
In Lightning Experience: Setup | Email | Deliverability
 

2. On the 'Access level' under the 'Access to Send Email (All Email Services)' section, select All email.

After changing this setting, the 'Send Email' button becomes available from the 'Activity History' related list in Classic or as a Chatter action in Lightning.

Notes: 

• If the 'Access to Send Email' level in the organization is set to 'No Access' or 'System Email Only'. In the layout for Mobile & Lightning Actions, users can drag the Email button to Salesforce Mobile and Lightning Experience Actions, but the setting doesn't stick. Users will notice after saving, that the Email button didn't properly save to the layout. Set access level to 'All email' in Lightning to resolve.
• The 'Send Email' button is available in the Activities component (Accounts, Contacts, Contracts, Leads, Opportunities, and activity-enabled custom object records) and Chatter component (Cases) in Lightning Experience.
• Users can’t send emails associated with Cases from the Global Actions menu in Lightning.

See Also:  
Add Send an Email, Log a Call, New Event, and New Task Buttons to the Activity Composer
Set Up Send Later for Your Sales Reps