I guess I found it.
Did you already activate the sub path /vault within Vaultwarden configuration?
If not, ensure you set correct value inside /mnt/dietpi_userdata/vaultwarden/vaultwarden.env
DOMAIN=http://dietpi.example.com/vault
And this is the fitting configuration on lighttpd. I’m now able to open http://dietpi.example.com/vault/ (including the trailing slash)