Yes, Crocosmia can get rust.
The variety 'Lucifer' seems to be more susceptible than the common orange variety in my garden.
Mike

What I see on many of these year after year is mites. Look at yours closely, maybe with a magnifier. Then you will be able to see what you have.

Well, evidently you're both correct. Close inspection found mites, leaves look exactly like rust.

Thanks -- I always appreciate the help I get from forum folks.