The verb form in the sentence, "I will have run a mile by the time you return from the Lincoln Memorial." is future perfect.
The future perfect tense refers to the action that will have been done or completed in the future at some point. It is often used with timely expression.
Formation of the future perfect tense is as follow,
Subject + will have/shall have + past participle of verb (3rd form) + object.
For example:
She will have been here for four months during summer vacations.
Similarly, the given sentence, depicts the action of run would be complete in the future at a point. Further it follows with the formation of the tense.
