I have seen kitchen displays with cabinets of about 12" under dishwashers. Of course, those were standard machines, not tall tubs. You don't want the LT. It was the modernized James design, but there was no real provision for backwashing the cylindrical filter around the impeller so it was not able to deal with particulate matter.  The wash cycle was sort of limited, too with it basically starting to fill at the end of wash to overflow the wash water down the drain and at the end, fog the dishes with steam so that they dried in distilled water. It could operate as a gravity drain machine and was probably the only dishwasher that came in three sizes based on numbers of place settings. Oh, it had a wind up timer that you turned all the way around from the OFF position to the beginning of the cycle and it ticked back through the cycle to OFF, like a damn Norge dryer. Interesting, but not great.