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The Moto Z Droid doesn't explicitly claim that it supports USB Power Delivery, but when you connect it with the Verizon Vehicle Charger with Fast Charge Technology, it's pretty clear that USB Power Delivery is under the hood of Lenovo's TurboPower branded technology for this phone using Granite River Labs USB Power Delivery test software.

When connecting the Verizon Vehicle Charger with Fast Charge Technology to the Moto Z Droid using a USB Type-C to Type-C cable, the Verizon Vehicle Charger with Fast Charge Technology declares it can support 15 watts (5 volts @ 3 amps), 21 watts (7 volts @ 3 amps), 24 watts (8 volts @ 3 amps), 27 watts (9 volts @ 3 amps), 30 watts (12 volts @ 2.5 amps), and 30 watts (15 volts @ 2 amps).

The Moto Z Droid then initially requests 5 volts @ 3 amps from the Verizon Vehicle Charger with Fast Charge Technology.

The Moto Z Droid then asks the Verizon Vehicle Charger with Fast Charge Technology to identify itself and below we can see more details about the charger below.  

After the Moto Z Droid finishes discovering the identity of the Verizon Vehicle Charger with Fast Charge Technology, the Moto Z Droid then requests a whopping 27 watts (9 volts @ 3 amps) from the Verizon Vehicle Charger with Fast Charge Technology.  This is one of the highest power levels that we've seen being requested by a phone using USB Power Delivery.  Previously we had only seen this level of power requested by a phone when the Le Max 2 requested 24.3 watts (9 volts @ 2.7 amps) from the iVoler 75W USB Type C Charger with Power Delivery.

With 27 watts of charging available initially, we see that the Moto Z Droid takes about 30 minutes to charge the battery by 50%, 50 minutes to charge to 75%, and 80 minutes to fully charge (note the power used when the battery closer to full is a lot lower and thus charging becomes a lot slower).