Does Greg Lestrade know/guess that Sherlock is alive?
In the Many Happy Returns trailer to Season 3, he grins at the headline "The Game is back on".
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Sign up to join this communityI see no evidence that Lestrade believes that Sherlock is alive, in fact, throughout the trailer he's quite adamant that Sherlock is dead and that any theories of him being alive are ridiculous.
Any grin would just have been at a rueful memory of things Sherlock might say.
Indeed, he continues to consider Sherlock as dead until The Empty Hearse episode or as he puts it when another possible escape from death scenario is put to him.
"Bollocks".