I'm not an expert at lighthttpd, but it would seem that your configuration files has a setting like this:
Code:
compress.cache-dir = "/var/tmp/lighttpd/cache/comp"
Now, the directory referred to in this configuration statement doesn't exist, which is why lighthttpd is complaining and refusing to start.
The solution may be as simple as just creating this path, like this:
Code:
mkdir -p /var/tmp/lighttpd/cache/comp
And then attempt to start it again. Otherwise, you might have to find a different/correct path for compress.cache-dir.