  In this paper, we initiate the study of sub-pluriharmonic curves in
Cuntz-Toeplitz algebras and free pluriharmonic majorants on noncommutative
balls. We are lead to a characterization of the noncommutative Hardy space
$H^2_{\bf ball}$ in terms of free pluriharmonic majorants, and to a Schur type
description of the unit ball of $H^2_{\bf ball}$. These results are used to
solve a multivariable commutant lifting problem and provide a description of
all solutions.
