In Shakespeare's A Midsummer Night's Dream, Duke Theseus most significantly influences the lives of the four Athenian lovers, Hermia, Lysander, Helena, and Demetrius.
In the opening scene, Duke Theseus expresses doubt that Egeus is making the correct decision in forcing his daughter Hermia to marry Demetrius upon punishment of death or exile. He expresses this doubt in response to Lysander's protests that he is just as wealthy as Demetrius, maybe wealthier, and that Demetrius is unfaithful. We observe Lysander accuse Demetrius of unfaithfulness in the following:
Demetrius, I'll avouch it to his head,
Made love to Nedar's daughter, Helena,
And won her soul; and she, sweet lady, dotes,
Devoutly dotes, dotes in idolatry,
Upon this spotted and inconstant man. (1.1.106-10)
Upon hearing Lysander's accusation against Demetrius of unfaithfulness, Duke Theseus expresses his doubt in the rightness of the match when he replies, "I must confess that I have heard so much, / And with Demetrius thought to have spoke thereof" (111-12).
He then takes Egeus and Demetrius aside to speak with them privately, probably to dissuade them from pursuing the match.
Therefore, by the time we reach act 4, scene 1, Duke Theseus is very willing to overrule Egeus's decision to force his daughter into marriage, and it his willingness to overrule Egeus that significantly influences the lives of the two Athenian couples. Theseus overrules Egeus's command the moment Theseus hears Demetrius explain that he is now in love with Helena, which Theseus believes is morally correct. Once he overrules Egeus's command to his daughter, he grants both couples permission to be married in the temple alongside himself and Hippolyta, as we see in the following:
Egeus, I will overbear your will;
For in the temple by and by with us
These couples shall eternally be knit. (4.1.176-78)
By permitting Hermia to marry Lysander and Demetrius to marry Helena, Theseus is significantly influencing their lives, especially by preserving the lives of Hermia and Lysander.