Here, the speaker is simply looking down a lane, or small street, that seems sad. Of course, we know that streets don't have feelings, but the speaker of this poem is so sad that even the street seems sad to him.
We don't get any details about what makes this lane so sad. We can imagine that the houses are all boarded up, that there are no people there, or maybe the street is strewn with trash – but this is left up to us. All that we know from the poem is that we're seeing this street at night, and it's sad.
The street is not only sad, but it's the saddest. This is similar to how the city light was not only far, but the furthest. The speaker wants to let us know that the kinds of nights he's writing about are not just your average dark and lonely nights, but the darkest, the loneliest.
I have passed by the watchman on his beat
The speaker has walked by the watchman, who is probably some sort of policeman or security guard.
The watchman is "on his beat," which is another way to say that he's on duty, making his normal rounds.
This is the only point in the poem where the speaker is in the physical presence of another person, even though he's in a city. Still, a policeman isn't the friendliest person to walk by on a dark, lonely night. This watchman seems to be just as cold and distant as everything else in the poem.
And dropped my eyes, unwilling to explain.
The speaker looks down, avoiding the glance of the watchman, because he doesn't want to explain something. We're not told what he's unwilling to explain. Maybe he's doing something that he shouldn't be doing, or maybe he is just so trapped in his own loneliness that he doesn't want to have to face another person.
This line dashes any hope we had of the speaker making contact with another person, and making his night a little less lonely. The speaker is shy, and walks by, trying to escape being noticed.
The speaker is also unwilling to explain something to the watchman, just like a lot of this poem is left unexplained for the reader. We don't know exactly where our speaker is, or why he's walking around at night, and, in this line, we don't even have an explanation for why we don't have an explanation! Looks like we'll have to just use our imaginations.