Cannot see expected files and attachments on Account records in Lightning

In Salesforce Classic, the Notes and Attachments related list on an Account record displays attachments from the Account itself as well as from related records such as Contacts and Opportunities associated with that Account. This roll-up behavior is a feature of Salesforce Classic.
In Lightning Experience, this roll-up behavior does not exist. The Notes and Attachments related list on an Account record shows only the files and notes directly attached to that Account record. Files attached to related Contacts or Opportunities are visible only on those individual records.
Example Scenario:

• John creates an Account called Acme and adds an attachment called Attach 1
• John creates a Contact called Acme Contact associated with Acme and adds Attach 2
• John creates an Opportunity called Acme Oppty associated with Acme and adds Attach 3

In Salesforce Classic, the Notes and Attachments related list on the Acme Account shows all three attachments: Attach 1, Attach 2, and Attach 3.
In Lightning Experience, the same related list on the Acme Account shows only Attach 1. Attach 2 and Attach 3 must be viewed on the Contact and Opportunity records respectively.
Lead Conversion Behavior:
This same behavior applies when converting Leads with attachments in Lightning Experience:

1. Create a Lead and add an attachment (visible under Notes and Attachments in Classic)
2. Convert the Lead and associate it with an Account
3. Open the Account in Classic — the attachment from the Lead is visible
4. Open the Account in Lightning Experience — the attachment does not appear

Note: Files uploaded using the Upload Files button in the Files related list in Lightning Experience do not roll up during Lead conversion, regardless of org settings.