Originally posted by .a.t. So you're saying I may as well chase my tail? ...
Probably not. I've been working on a (private) catalogue of K-mount lenses since 2013, collecting pictures of almost 5000 lenses and variants of lenses. Doing so, I have come across 2 totally different 135/2.8 lenses in 8 variants in Sears brand, albeit I have never seen the specific one shown in the image you posted.
It appears that Sears had made their 135mm lenses by Tokina and Samyang. Here are the lenses I know of:
Japan (most likely Tokina):
Auto Sears MC 135mm 1:2.8 (K) : 199.730590, S/N 100nnn-???nnn, Different shape with double aperture scale
Auto Sears MC 135mm 1:2.8 (K) : 199.730670, S/N 100nnn-105nnn, Different DOF scale
Auto Sears MC 135mm 1:2.8 (K) : 199.730670, S/N 106nnn-???nnn, Different aperture ring
Korea:
Auto Sears 1:2.8 f=135mm (K) : Mod.No. 202.730590, S/N 21nnnn-22nnnn, Mod.No. 202.730590
Auto Sears MC 1:2.8 f=135mm (K) : Mod.No. 202.737370, S/N 819nnn, 822nnn, 832nnn, 852nnn, 864nnn, 879nnn, 888nnn, 922nnn,
Auto Sears Multi Coated 1:2.8 135mm (K) : Mod.No. 202.737370, S/N 840nnnnnn,
Auto Sears Multi Coated 1:2.8 135mm Macro (K) : Mod.No. 202.736950, S/N 840nnnnnn, 841nnnnnn,
Auto Multi Coated 1:2.8 f=135mm (KAR) : Mod.No. 202.7368100, S/N 860nnnnnn, 870nnnnnn,