Is it possible to identify the User (Name or Email) of the person who performed a Lazy Approval in Office 365 for auditability. For example, the nominated Approver may forward the email on to another user who then does a Lazy Approval, we need to capture who Approved the Document and log this to either the Workflow History or in the Checkin Comments for the document.
If you are using 'Assign Flexi task' action or 'Approval Task', who ever the approver it should go to either approve or reject case like below.
So using 'Set Variable' action click on insert reference and select 'Initiator's Display Name' or 'Last Task Respondent Display Name'
So use 'Log in History action' and check approver name is coming correctly or not and use that.
For approver comments use 'Approver Comments' from insert reference as mentioned by Fernando Hunth.