Spell save DCs are based on the class with which a spell is associated
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Generally, every spell you acquire will be a result of a feature/levelling up of a particular class. That spell will be associated with that class and will use the spellcasting modifier for that class for the DC when you cast it.

This is explained in the [multiclassing rules][1]:

> Each spell you know and prepare is associated with one of your
> classes, and you use the spellcasting ability of that class when you
> cast the spell.

Now, Warlock invocations are a bit of an edge case perhaps. But by omission, a spell cast via an invocation is still a Warlock spell and hence would use Charisma to calculate any save DC. I'll admit to not being 100% sure of my own statement here!

  [1]: https://www.dndbeyond.com/sources/basic-rules/customization-options#Spellcasting