With "as" a conjunction connecting two independent clauses, I, too, would be inclined to insert a comma. However, I can't exactly say that that current construction is right. Here's why:
"Amanda said" (&c.) is an independent clause. The quotation is merely an extension of it. So, we have "'The sound is almost deafening,' Amanda said." This makes grammatical sense by itself.
Also an independent clause is "they continued down the narrow lane." The word "as" acts as a subordinating conjunction—that is, the addition of "as" to the second half creates a dependent clause: "as they continued down the narrow lane." This clearly can't stand by itself; it needs another half to connect to.
When you join it with an independent clause before it (as it does in your examples), you end up with an I.C. followed by a D.C., which does not require a comma. Were the I.C. to follow the D.C. ("As they walked down the lane, Amanda said, 'The sound is almost deafening'"), you would definitely need a comma.