There are multiple concepts involved here, from different sources.
The ASIL levels are defined by ISO 26262. ASIL-D is the highest level and using a lockstep CPU is one of the methods typically used to achieve ASIL-D compliance for the whole system. Autosar doesn't define how you achieve ASIL-D, or any ASIL level at all. From an Autosar perspective, lockstep would be an implementation detail of the MCU driver, and Autosar doesn't require MCUs to support lockstep. How a particular lockstep implementation works (whether the outputs are compared after each instruction or not, etc.) depends on the hardware, so you can find those answers in the corresponding hardware manual.
Correspondingly, some decisions have to be made by people working on the system, including an expert on functional safety. The decision on what to do on lockstep failure is one such decision - how you react to a lockstep trap should be defined at the system level. This is also not defined by Autosar, although the most reasonable option is to reset your microcontroller after saving some information about the error.
As for where in the Autosar stack the trap should be handled, this is also an implementation decision, although the reasonable choice is for this to happen at the MCAL level - to the extent that talking about levels even makes sense here, as the trap will run in interrupt/trap context and not the normal OS task context. Typically, a trap would come with a higher priority than any interrupt, and also typically it's not possible to disable the traps in software. A trap will be handled by some routine that is registered by the OS in the same way it registers ISRs, so you'd want to configure the trap handler in whatever tool you're using for OS configuration. The lockstep trap may (again, depending on the hardware) be considered a non-recoverable trap, meaning that the trap handler should trigger a reset eventually. Calling the standard ShutdownOS() function may be reasonable.