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While reading the book "The Feather Thief" (by Kirk Wallace Johnson; quite fascinating), I've come across the hyphenated compound "fly-tier", referring to one who ties flies for fishing. Since the subject is fly-tying, why is this spelled "tier" rather than "tyer"? I'm more familiar with "tier" referring to a level in a stack, or (with an initial cap) a German beast.

In the sense of tying, the questioned spelling occurs in this forum as "tongue-tier" in an entry for "phthisic" (I'm not about to disagree with that). But "tier" as a level is much more common, is pronounced differently, and can also appear in a hyphenated compound, e.g., "top-tier". Dictionary treatment is unsatisfying, sometimes being given as "variant of tyer", but nothing more definitive is given for "tyer".

Without context, it's anybody's guess what might be meant.

One of those awkward situations, no? Both are acceptable, yet problematic. Me for the coward’s exit strategy: find an alternative.

The OED has examples of tier in the sense of tyer from 1633 to 1847 and no mention of "archaic" or "obsolete" or "US" vs. "UK", or "dialectal". This implies that both are acceptable.