The current Lexus LX is known officially in North America as the LX 600. CarBuzz happened to find filings for a Lexus LX 700h with the Canadian Intellectual Property Office. CarBuzz is assuming the LX 700h will have a derivative of the Tundra i-Force Max instead of the LS 500's 3.4L Turbo and then add a motor. They are also of the opinion that it should be a plug-in hybrid. It's a rather humorous read on what they think a typical LX driver needs and, in CarBuzz eyes, its not off-roading. Lexus LX700h Coming As Range-Topping Hybrid For Luxury Off-Road SUV | CarBuzz
It is a full size truck. Using an Atkinson engine would require a more powerful motor to make up for that loss. That will increase the cost. It will very likely be the drive train from the Tundra and Sequoia hybrids. Those use a turbo engine with a 10.4:1 compression ratio with variable valve timing. It could approach Miller cycle operation, which is basically Atkinson with a charger.
Doesn't Toyota have those 4 cylinder engines that can run Atkinson at low loads and Otto in power mode? Or is that even more complicated with a hybrid system?
That is a wide variable valve timing system. The wide refers to the difference between Otto and Atkinson cycles. It does have a higher cost, and the benefit is limited on a hybrid compared to an ICE model. The money for the Tundra hybrid engine went to the dual injection. It is Otto cycle cause some people buying trucks still do truck things with them.