Load Balancing on basis of Source IP in BIG IP F5 LTM

I'd recommend the iRule route myself. The only real alternatives are to give your 'demanding' client a different domain name that resolves to a different Virtual Server IP or possible use a different port so you can configure a dedicated VS for them. A HTTP Class might also be an option allowing you to keep the same domain name and VS but this is only workable if you can identify the client in some unique way using the URI, not source IP address.