When a gas is in LTE then the absorption and emission is isotropic, but when Milne came up with the idea of LTE he wrote «This permits us to see in a general way why the state of local thermodynamic equilibrium in the interior of a star breaks down as we approach the surface.» (realclimate.org)
So, a system at Local Thermodynamic Equilibrium doesn't change temperature. (wattsupwiththat.com)
It is the strong absorbers that are also the strong emitters; the backradiation comes overwhelmingly from those strong absorbers (which are in very close to local thermodynamic equilibrium with the bulk gas). (wattsupwiththat.com)