We measure the inclusive forward-backward asymmetry of the charged-lepton pseudorapidities from top-quark pairs produced in proton-antiproton collisions, and decaying to final states that contain two charged leptons (electrons or muons), using data collected with the Collider Detector at Fermilab. With an integrated luminosity of 9.1 $rm{fb}^{-1}$, the leptonic forward-backward asymmetry, $A_{text{FB}}^{ell}$, is measured to be $0.072 pm 0.060$ and the leptonic pair forward-backward asymmetry, $A_{text{FB}}^{ellell}$, is measured to be $0.076 pm 0.082$, compared with the standard model predictions of $A_{text{FB}}^{ell} = 0.038 pm 0.003$ and $A_{text{FB}}^{ellell} = 0.048 pm 0.004$, respectively. Additionally, we combine the $A_{text{FB}}^{ell}$ result with a previous determination from a final state with a single lepton and hadronic jets and obtain $A_{text{FB}}^{ell} = 0.090^{+0.028}_{-0.026}$.
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