Answer
All its diagonal entries must be nonzero
Work Step by Step
The transpose of a square lower triangular $n\times n$ matrix is
an upper triangular $n\times n$ matrix.
By the last exercise, $A^{T}$ is invertible when all its diagonal entries are nonzero.
But, $A$ and $A^{T}$ have the same diagonal entries, and
by Th.8 (a) and (l) if one is invertible, so is the other,
our conclusion is that in order for $A $ to be invertible,
all its diagonal entries must be nonzero
