Well, since you are using Python, you can just open a file and keep reading lines from it.
f = open('file.log')
If the line read is not empty, you process it.
line = f.readline()
if line:
// Do what you want with the line
You may be missing that it is ok to keep calling readline
at the EOF. It will just keep returning an empty string in this case. And when something is appended to the log file, the reading will continue from where it stopped, as you need.
If you are looking for a solution that uses events, or a particular library, please specify this in your question. Otherwise, I think this solution is just fine.