Wilt -- This helping verb "will" indicates that the verb is the future tense. Helping or auxiliary verbs are needed to translate the Greek verb forms into English.

thou -- This is from the second-person, singular form of the verb.

lay down -- The Greek verb translated as "lay down" is translated from a Greek word that means primarily "to put," "to dedicate," "to assign," "to award," and "to place," and in the military, "to bear arms," "to lay down and surrender," but which has many related meanings as well.

thy -- The word translated as "thy" is the genitive form of the singular, second-person pronoun, which is most commonly the possessive form. This pronoun follows the noun so "of yours."

missing "the/this"  -- (MW) The untranslated word is the Greek definite article,"the," which usually precedes a noun and, without a noun, takes the meaning of "the one." The Greek article is much closer to our demonstrative pronouns ("this," "that," "these," "those"). See this article for more. 

life - (CW) -The word translated here as "soul" is life, a common word in Greek, familiar in English, meaning "life," "soul," "consciousness," and "a sense of self." It is used for different aspects of "self," the emotional self, the conscious self, the intellectual self. It has a clear sense of the conscious self and is often translated as "life" in the Gospels. Jesus uses it to specifically mean our identity in our worldly life, the role we play on earth, what we might call the "social self," or what we commonly call our "ego." See this article for detail about this word.

for -- "For" is a preposition that means "over" "beyond," "concerning," "on behalf of,"  and "instead of" with many other specific uses.

my -- "My" is the first-person possessive singular pronoun.  As a genitive object of a preposition, as here, it means a movement away from something or a position away from something else.

sake? --  This completes the idea of the preposition.

Verily, -- The word translated as "verily" is from the Hebrew word that means "truly" or "certainly," but it sounds like the Greek word with the same meaning. In Greek, the word also means "to reap."  See this article discussing this "amen phrase."

verily -- The word translated as "verily" is from the Hebrew word that means "truly" or "certainly," but it sounds like the Greek word with the same meaning. In Greek, the word also means "to reap." See this article discussing this "amen phrase."

I -- This is from the first-person, singular form of the following verb.

say -- The word translated as "say" is the most common word that means "to say," and "to speak," but it also means "to teach," which seems to be the way Christ uses it more frequently. It also has many ancillary meanings such as "to count" ("to number" or like we might say, "to recount" a story) or "to choose for yourself." Christ usually uses this word to refer to his own speaking or teaching.

unto -- This word "unto" comes from the dative case of the following word that requires the addition of a preposition in English, but the translator must decide which preposition to use: a "to" as an indirect object.

you,  -- The Greek pronoun "you" here is singular and in the form of an indirect object, "to you," "for you," etc.

The -- (IW) There is nothing in the Greek that can be translated as "the" in the Greek source. A singular noun without a definite article should have an indefinite article, "a" not the definite article, "the."

cock - The word for "cock" means a "rooster" and also a "husband."

shall -- This helping verb "shall" indicates that the verb is the future tense or a form that indicates possibility at some time. Helping or auxiliary verbs are needed to translate the Greek verb forms into English.

not -- (CW)  The "not" here is both of the Greek negatives used together. Greek has two negatives, one objective, one subjective. The use of both together is more extreme, like saying, "never" or literally, "you cannot really think." When a negative precedes the verb, it affects the whole clause. When it precedes other words, its force is limited to those words.

crow, - -- (CW) The word translated as "crow" simply means "to utter cries."  It means the cries of animals, but it also refers specifically to someone calling another name. Jesus uses it both for the voice of people and the calls of animals.

till -- The word translated as "till" means "until" but it also means "till," "while," "as long as," "in order that."  With the particle of possibility and the subjunctive form of the verb, the sense is until some unknown time.

missing "this"  -- (MW) The untranslated word "this" is a demonstrative pronoun ("this" "that"), but it often acts as a pronoun "which," "what," "who," "whosoever," "where," "for which reason," and many similar meanings.

thou -- This is from the second-person, singular form of the verb.

hast -- (WW) This helping verb "have" indicates that the verb is the tense indicating an action completed in the past. This is not the tense of the verb here. This is either the future tense requiring a "will" or a subjunctive, requiring a "might."

denied -- "Deny" is translated from a Greek word that means "to reject" and "to deny utterly." The form is either the future tense or a tense meaning something that might happen at some specific time, past, present, or future. If the word is the "at some time" tense, it is in a form that indicates something that "might" happen. This later "might at some time" form is always used with "if" clauses, which is the sense here.

me -- "Me" is the regular first-person pronoun in Greek as the object of the verb or preposition.

thrice. "Thrice" is a word that means "three times" and "thrice."