AFAIK GMH didn't option any LHD LH/LX with L31 & M40.
Yes, you're probably correct there.
It's one of those anomalies. GM-H lists these boxes in various different publications. Parts catalogues, service bulletins, various supplements & service notes & often they don't always agree 100%.
This is a good example. Several Trimatic service bulletins list KL as being a series 2 LHD transmission to suit both 4.2 & 5.0 V8. There is a part supplement which also says the same thing. BTW the KL Trimatic has the part no. 9930272.
As far as I am aware it's not too often that the same box suits both a 4.2 & a 5.0.
However the LH parts catalogue lists this box as LHD V8, with no mention of engine size. This same catalogue in its intro page lists what you say, i.e. no LHD L31/M40.
Reading between the lines, it probably means that the KL is for LH 4.2 LHD only.
Dr Terry