English translation:
Already
too late
Structure:
すでに + Phrase
硬
In this sentence:
時すでに遅し。
What grammatical construct is 遅し (おそし)?
And why is no particle used after 時?
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Hey 
It is a set phrase.
遅し is くadjective in predicative form (the form used on the end of the clause, not the form used to modify nouns, in classical Japanese predicative and attributive forms were different for adjectives (more here))
く adjectives are basically ancestors of modern い adjectives.
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Here and elsewhere the translation of 既に is almost always ‘already’ even when ‘too late’ could be meaningful. Is it due to the way how this word is really understood and used by Japanese? Is there another word to say ‘too late’ without ambiguity?
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The basic meaning is always ‘implying something absolutely cannot be changed’. So rather than losing one of the meanings, its really the same one being changed around to better fit a translation.
Hope this helps!