EA has discontinued Legacy edition on January, so it wont even open on my iMac Late 2006 and as result I cant download my packs, I do have them in disks but some of my disks doesn't work like Uni, so I have to download from Origin. Now I can't because it doesn't support Lion and my iMac can't go further than Lion. I do have a PC running 7 but I much prefer playing on my iMac because is a smoother experience overall.
I do know that I can run Windows on Mac but I don't want to dualboot on my iMac for now because the hard drive is too small for that. Also I already everything set up Sims 3 set up on macos and I don't feel like passing everything to Windows.
How can I download my packs now?

You can't. But since you are running an operating system that still supports the retail disc authentication, which is not the case for those on El Capitan or higher, what you can do is purchase some new (to you) discs from retail sources or re-sellers to replace the ones that are now not working. Although that may not seem fair, it is exactly the same situation someone on a 14 year old system would be in if Origin never even existed.

Do you still have a disc reader? I'd just burn the discs to ISOs.

I'm forever forgetting where I store the discs and have since 2010 always created ISOs and store those files and the keys in my HDD storage archives. Same thing goes for those legacy apps that takes me an age to look for on the web. Except when that particular HDD was making noises and failing. Guess what files I ensure to have a working backup+restore workflow first?