  We study the asymptotics of bounded lecture hall tableaux. Limit shapes form
when the bounds of the lecture hall tableaux go to infinity linearly in the
lengths of the partitions describing the large-scale shapes of these tableaux.
We prove Conjecture 6.1 in \cite{SKN21}, stating that the slopes of the
rescaled height functions in the scaling limit satisfy a complex Burgers
equation. We also show that the fluctuations of the unrescaled height functions
converge to the Gaussian free field. The proof is based on new construction and
analysis of Schur generating functions for the lecture hall tableaux, whose
corresponding particle configurations do not form a Gelfand-Tsetlin scheme; and
the corresponding dimer models are not doubly periodic.
