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This might be a really dumb question, but does a Lord of Change get any kind of save? I'm new to Chaos Daemons, so maybe I'm just reading it wrong, but I don't see anything that give him a save.

The rule you are over looking is daemonic alignments.

Daemonic alignments grant a whole bunch of special rules, with the Daemon special rule being universal across all four. If you look on page 35 of the basic rule book you will find what the daemon special rule actually does. I do not post rules directly to this board, no one should as they can be considered copy written material, but I can state that all models with the Daemon special rule are granted a invulnerable save and you will find what the save actually is on page 35.

A Lord of Change has a 5+ invulnerable save baseline.

It can get a 3+ armour save and a 4+ feel no pain from Greater Gifts and it can get re-rolls to failed invulnerable saves as well.

It can also have its invulnerable save improved or made worse by the Warpstorm Table and the Grimoire of True Names.

The only save listed in a model's profile is the Armour Save. Since a LoC doesn't have an armour save, the Sv characteristic is listed as '-'
As Jinx said, you're looking for the Daemon USR, which grants an invuln.

DERP... yeah, I missed that Daemon USR in the alignment section.