I have some Unifi AP-LR with Firmware 3.2.12.2920. The automatic Update not working. So here is the manually way:

Login to the AP with SSH (putty or WinSCP)

Download the oldest available firmware (3.7.58.6385) and upgrade the AP (use http, https only work after upgrading to 3.7.58)

rm /tmp/fwupdate.bin
wget http://dl.ubnt.com/unifi/firmware/BZ2/3.7.58.6385/BZ.ar7240.v3.7.58.6385.170508.0942.bin -O /tmp/fwupdate.bin
syswrapper.sh upgrade2 &

After upgrading the firmware to 3.7.58.6385 the automatic upgrade work again, also the https links are working now.
upgrade 3.7.58.6385 to 4.0.10.9653
upgrade 4.0.10.9653 to 4.0.54.10625