As with any definition question, the place to start is by examining the word in its context and seeing if you can pick up any contextual clues. Let us think about the line in which this word appears:
"Surely," said I, "surely that is something at my window lattice..."
It is obvious then that lattice has something to do with window, and the tapping is "at" the "window lattice." Using a process of elimination would suggest that it could not be a lock. You cannot "tap" at a lock very easily. This leaves the other three as possible responses. Actually, a lattice is a shutter or screen formed by strips or bars overlaid in a criss-cross pattern, so none of your answers are strictly correct.