Professor not responding to LOR email after initially agreeing
I'm not sure if I'm reading too much into it.


I think you are.

My guess is that Professor #2 received your email, saw that it contained information for your letter, remembered that he had already told you he would write the letter, and set the email aside, planning to read it in detail when he got around to actually writing the letter.  He probably didn't read far enough to see the part where you asked him to acknowledge the email.

So, if you're concerned, simply send a second email:


  Dear Dr, #2,
  
  I just wanted to make sure you had received my email of August XX with the information for my letter of recommendation.  Please let me know if it looks okay, or if there is anything else you need.  As a reminder, the deadline to submit the letter is October XX.
  
  Thanks very much for writing a letter for me!
  
  Sincerely,
  
  Lily


As to your other question:


  I accidentally called this second professor "Professor" in my email even though he's technically a lecturer so I always address him as "Dr. So-and-so" in my emails.


Don't worry about that.  It happens all the time and most professors eventually just stop noticing.  It's certainly not the kind of thing that would offend someone so much as to affect their decision to write a letter.