will my Handspring LifeDrive PDA work after the Yosemite upgrade?

If it will not run in Lion is will also not run in Yosemite.

This presumably uses the Palm Desktop; this hasn't been updated for years and won't run on anything higher than Snow Leopard (because it's PPC). I'm afraid all Palm devices are now well obsolete unless you can continue to maintain Snow Leopard, perhaps by maintaining a separate Snow Leopard volume or partition to boot into (at least as long as you can keep an older Mac running - you can't do this on a new Mac). Though it's theoretically possible to run Snow Leopard Server under emulation in Parallels, I doubt the background syncing processes will work this way.

You will need to start thinking of how to move away from Palm to more modern devices: this article may help -

http://www.wilmut.webspace.virginmedia.com/notes/palmtomac.html

MissingSync

<http://www.markspace.com/>

has sync'ing software for Palm based products. I've used it for my Sony CLIE (Palm based) PDA up to and including, Mavericks. I do not see any reason why it would not work on Yosemite.

But ask them, and I'm sure they will tell you.