Most places never ever ever ever update iLO or other out of band management system unless there's new firmware. This results in fun stuff like needing three or four old versions of java and older browsers, and certs that are expired.
If there's an updated firmware it may support more modern browsers and SSL, but I wouldn't hold my breath.
The alternative is to grab an older browser just for this. This Security.SE post says that Firefox 33 Portable will work on Windows. It's going to be a minor pain if you need Java et al.
You can sometimes also run older (or newer) browsers alongside current versions - not sure how this works on a Mac, though. Basically, you need a browser that hasn't disabled SSLv3 or will let you enable it alongside your current one.
Personally, I'd rather run a full install, configured on a VM, and you can find older versions here. Configure, get it working and disable updates. However, and I've not tested this, you can also run Firefox versions side by side with a little work. Apparently this involves copying out and renaming the .app from the dmg (cool trick!), and then explicitly creating a profile using that version, and fixing up the link to it. Not tried it yet.
The VM option sounds better, since you can build an entire environment with Java versions and other prerequisites other than the browser, but your mileage may vary.