In 'Othello' Iago, the ensign has a love life of his own. He loved to become a general in the army of venice. But Othello chose Cassio in stead of Iago and so he resolved to revenge upon Othello. To succeed in his mission he took help of various intrigue which ultimately brought him success. He created such a situation that Othello killed Desdemona with his help and later on Othello also died.
According to the story of the book 'Heccatommithi' by cinthio, an Italian novelist from which Shakespeare took the plot of Othello; the ensign(Iago) loved Desdemona and when she did not pay any respect to his love, he vowed to prove her infidelity.
Although he exploits the amorous passions of both Roderigo and Othello, but appears to have no romantic inclination himself, Iago does have a love life which is Desdemona's older servant lady, Emilia.
I don't know if you can say Iago really has a "love life." But, he is married to Emilia, who is Desdemona's "lady-in-waiting." Iago doesn't have much respect for women. In Act II, Scene I, when Iago is talking with his wife and Desdemona, and he is says some very unflattering things about women in general Lines 118-124.
Iago is an unhappy man. He spends the book trying to bring down someone else by weaving this web of lies. I'm sure his "love life" with Emilia is hardly considered that. mm