We study the formation and collision-aided decay of an ultra-cold atomic

Bose-Einstein condensate in the first excited band of a double-well 2D-optical

lattice with weak harmonic confinement in the perpendicular $z$ direction. This

lattice geometry is based on an experiment by Wirth et al. The double well is

asymmetric, with the local ground state in the shallow well nearly degenerate

with the first excited state of the adjacent deep well. We compare the band

structure obtained from a tight-binding (TB) model with that obtained

numerically using a plane wave basis. We find the TB model to be in

quantitative agreement for the lowest two bands, qualitative for next two

bands, and inadequate for even higher bands. The band widths of the excited

bands are much larger than the harmonic oscillator energy spacing in the $z$

direction. We then study the thermodynamics of a non-interacting Bose gas in

the first excited band. We estimate the condensate fraction and critical

temperature, $T_c$, as functions of lattice parameters. For typical atom

numbers, the critical energy $k_BT_c$, with $k_B$ the Boltzmann constant, is

larger than the excited band widths and harmonic oscillator energy. Using

conservation of total energy and atom number, we show that the temperature

increases after the lattice transformation. Finally, we estimate the time scale

for a two-body collision-aided decay of the condensate as a function of lattice

parameters. The decay involves two processes, the dominant one in which both

colliding atoms decay to the ground band, and the second involving excitation

of one atom to a higher band. For this estimate, we have used TB wave functions

for the lowest four bands, and numerical estimates for higher bands. The decay

rate rapidly increases with lattice depth, but stays smaller than the tunneling

rate between the $s$ and $p$ orbitals in adjacent wells.