Representing Z/NZ as roots of unity, we restrict a natural U(1)-action on the
Heegaard quantum sphere to Z/NZ, and call the quotient spaces Heegaard quantum lens spaces.
Then we use this representation of Z/NZ to construct an associated complex line bundle. This
paper proves the stable non-triviality of these line bundles over any of the quantum lens spaces
we consider. We use the pullback structure of the C∗-algebra of the lens space to compute
its K-theory via the Mayer-Vietoris sequence, and an explicit form of the Bass connecting
homomorphism to prove the stable non-triviality of the bundles. On the algebraic side we
prove the universality of the coordinate algebra of such a lens space for a particular set of
generators and relations. We also prove the non-existence of non-trivial invertibles in the
coordinate algebra of a lens space. Finally, we prolongate the Z/NZ-fibres of the Heegaard
quantum sphere to U(1), and determine the algebraic structure of such a U(1)-prolongation.