Are the signals BT_DEV_WAKE and BT_HOST_WAKE required to be connected to the host on designs with Laird's Sterling-LWB and -LWB5 Wi-fi modules?

The signals BT_DEV_WAKE and BT_HOST_WAKE are only enabled when the modules entered Low Power Mode(LPM). Hence the signals are only mandatory to be connected to your host when LPM is planned to be used. However, if enough GPIOs are available it is always a good idea to have those signals connected to the host processor.

Please check the LWB Datasheet or the LWB5 Datasheet for the status and polarity of each signal in the various states.