Call your CFO and ask if they have even received anything for you first. I was waiting 4 weeks for my LATT also, only to find out when I called that my range had not even submitted the request for it yet. After finding that out I called and Emailed the range a little ****** off, they apologized for the delay and sent it in right away, a day or 2 later they Emailed me a copy of the LATT number.
So it does not take long at all on the CFO side, but like mentioned it depends on when your range/club actually submits a request for you, so check that has been done or you could be waiting for nothing like I was. A lot of clubs use volunteers so they are busy and things get delayed at times, or so Ive been told lol