Motability Scheme respond to questions about whether the DWP will continue to transfer payments for Motability leases while customers are self-isolating.
Frequently Asked Asked Questions here

Lease payments will continue as usual.
Cars are vital to enable customers to get out for medical appointments, prescriptions and buying food, should you need to change your named driver(s) to allow another friend or family member to use the vehicle to help in these circumstances they can do so quickly.

Find out more information about changing the named driver here.