Is it mandatory to add the 32.768kHz oscillator (LPO) for SUSCLK to my LWB5+ design?

The external LPO is absolutely required. ​Firmware is configured to expect that, and the radio won't operate without it.

The low power oscillator is not used for just sleeping. It is also typically the clock source for the PMU, which is the first thing that has to be active and handles the reset sequence and other things as well.
The name “Low power” just distinguishes it from the “main” clock source, which runs much faster and draws much more power.  The main oscillator can be stopped in various scenarios to conserve power, but there will always be a clock source active to do tasks that are always necessary, and that one will be low power.

To correctly add a suitable LPO please refer to the reference schematics avaílable on the landing page of the Sterling-LWB5+ under "Technical Drawings" and the datasheet available under "Datasheet".