For LotR SBG with the 1/3 bow rule limit:

Is the bow limit per each alliance taken (for each LOME alliance, for every archer you take, you must take 2 non-archer warriors)?

Or is the bow limit an overall limit for all warriors fielded?

For example, in an Arnor - Rivendell alliance, can I take:
Rivendell Elf Captain + 10 Elf Warriors (no bows)
and then take
Arnor Captain + 10 Warriors of Arnor + 10 Rangers of Arnor

Overall I have 1/3 bows, but from the Arnor Alliance, I have a 50% bow ratio.

Would this be a legal army list to use?

Nope.

The 1/3 (or 33%, depending on which part you read) rule is per allied force.

In your above example, you would need 20 Warriors of Arnor to field 10 Rangers.

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