The pair in lockstep is "close", in that it only includes the core and deterministic private resources like core private caches. Shared resources like a L3 cache are outside of the whole pair, and can be seen as accessed by the pair. All output is from the pair and checked for consistency (same for both cores in lockstep) before going out.

Not directly related but some platforms supporting lockstep are flexible: you can use a pair as either 2 cores (perf) or a single logical one (lockstep).