Depends on the tense of the work, and where the sentence is occurring.
All of these are correct:
"Who lives at 221B Baker Street?" asked the red-headed menace.
"Who lived at 221B Baker Street?" asked the red-headed menace [in 2011].
"Who lived at 221B Baker Street?" the red-headed menace asks.
If the narrator is speaking and the tense of the novel is present, then it's:
Who lives at 221B Baker street? Why, none other than Sherlock Holmes himself!
Otherwise, if the tense is in the past it's:
Who lived at 221B Baker street? Why, none other than Sherlock Holmes himself!
Or, if the narrator is speaking about events in the past, but Sherlock Holmes is still alive and well and living there (from the narrator's point of view), then perhaps:
Who lives at 221B Baker street? Why, none other than Sherlock Holmes himself! I remember the case of the red-headed menace quite well, it all began when...
but I'm not so sure about this one.