Webster’s 1913 has no entry under this spelling.
Shades of meaning
Fernald has no entry of its own for mete out; he lists it under allot.
Where he writes about it:
From signifying to superintend officially some application or infliction, administer passes by a natural transition to signify inflict, mete out, dispense, and blows, medicine, etc., are said to be administered: a usage thoroughly established and reputable in spite of pedantic objections. — from execute