An update.
I'm not sure why it was occurring previously, but subsequent restarts of the system have not lead to the /var/lib/misc folder being removed, and after a power cycle the system is running as expected. It may have been due to this solution as well (removing softAP0 file) FTL offline and pihole not blocking ads - #11 by deHakkelaar
Combined with this solution, FTL is offline after update to 4.0 - #27 by deHakkelaar everything appears to be working as expected.
To anyone else facing this issue: dnsmasq: cannot open or create lease file /var/lib/misc/dnsmasq.leases: Permission denied here is how I solved it.
sudo mkdir /var/lib/misc
sudo touch /var/lib/misc/dnsmasq.leases
sudo chown pihole:pihole /var/lib/misc/dnsmasq.leases
Then restart the service and everything should be well. Just ensure that it persists through a power cycle and you should be good to go.