Surprisingly enough, I got a reply from Anonymizer tech support on a Sunday morning, yet:

Dear Customer:

I am sorry however we do not support p2p programs at this time.

Anonymizer Support

Thank you very much for trying, but it's worth noting for future questions you might get regarding Anonymizer, especially since I have seen at least two posts that recommended using it. As of 6/12/05, you cannot use LimeWire through Anonymizer.

Thanks again.