  We use ku-cohomology to determine lower bounds for the topological complexity
of 2-torsion lens spaces. In the process, we give an almost-complete
description of the tensor product of two copies of the ku-homology of infinite
mod 2^e lens space, proving a conjecture of Gonzalez about the annihilator
ideal of the bottom class. Our proof involves an elaborate row reduction of
presentation matrices of arbitrary size.
