Answer
In order to enable LPM mode on the Sterling-LWB, Sterling-LWB5 and Sterling-LWB5+ modules the options --enable_lpm and --enable_hci need to be added to the patchram command line expression:
# patchram -d --patchram /lib/firmware/brcm/4343w.hcd --enable_lpm --enable_hci --no2bytes --tosleep 1000 /dev/ttyS1 c1 &
This also enables BT_HOST_WAKE (output) and BT_DEV_WAKE (input).
BT_DEV_WAKE needs to be asserted for the module to respond.