Theta Series of Lattices Associated with Hyperbolic Tilings

to my knowledge (more bibliographic details shortly) none of the theta series below occur in the On-Line encyclopedia of integer sequences, and "complex hyperbolic lattices" and "lorenzian lattices" appear to be different beasties.

Hyperbolic Lattice Point Problems by Fernando Chamizo
Non-Euclidean visibility problems by Fernando Chamizo Hyperbolic lattice-point counting and modular symbols by Yiannis N. Petridis and Morten S. Risager
An Exact Formula Relating Lattice Points in Symmetric Spaces to the Automorphic Spectrum by Amy T. Decelles
Counting Lattice Points by Alexander Gorodnik and Amos Nevo
Sphere Packings, Lattices and Groups by John Horton Conway and Neil Sloane
The Hyperbolic Lattice Point Count in Infinite Volume with Applications to Sieves by Alex V. Kontorovich
On the distribution of angles between geodesic rays associated with hyperbolic lattice points by Florin P. Boca
On the Critical Line of Convex Cocompact Hyperbolic Surfaces by Dimitry Jacobson and Fr\'{ed\'{erik Naud
Hyperbolic Geometry: Isometry Groups of Hyperbolic Space by Ilyas Khan.

Bounty: I am offering a bottle of whisky to anyone who can successfully translate Jacob Lurie's Higher Topos Theory (and/or the stacks project) into the analytic combinatorical language of the manner of Flajolet's Analytic Combinatorics.