But -- The Greek word translated as "but" joins phrases in an adversarial way. Since it always falls in the second position, translating it as "however" often captures its feeling better.

go -- (CW) "Go" is a verb that means "make to go," "carry," "convey," "bring," "go," "march," and "proceed." However, it is usually translated as "go" in the NT. It  could be in a command or or a statement in the past tense, but it is mores likely a statement in the present tense because that better matches the forms in the previous and next verses. This word, however, uniquely means both "to pursue a course" and "to depart from life." Since the verb acts on itself, the sense is "make yourselves go."

rather -- "rather" is from a comparative that means primarily "more," "to a greater degree," "more certainly," and then "rather." However, it is also a form of an adjective that means a "flock of wool," so it seems like it was chosen at least partly for wordplay.

to -- The word translated as "to" means "towards," "by reason of (for)," "against," and "on the side of," but it has a wide variety of uses including "like," which works best with the comparative that introduces it.

the  -- The word translated as "the" is the Greek definite article, 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. 

lost -- (WW) The word translated as "lost" is a Greek verb that primarily means to "destroy" or "demolish." It is the form of an adjective, used as a noun as an object of the sentence, introduced by an article ("the"). The sense is "the destroyed." Jesus uses this word in the sense of "losing" life not losing your way. Another verb is used in te Matthew describing the sheep in the parable of the lost sheep (Matthew 18:12) as "going astray." This word, however, is used in Luke in the parable of the lost sheep. In the Greek, this word appears after and article after the word "sheep" and is the word modified by the  "house of Israel" phrase, which follows it.

sheep -- The word translated as "sheep" refers to any domesticated four-footed animal. In the plural, as it is here, it is also in the form of an object of the sentence introduced by an article ("the"). In the Greek, it appears before "destroyed." Christ does not use the term "herd" ("sheep") in a negative sense.

missing "the"  -- (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." Here, it precedes the  word translated as "lost." The Greek article is much closer to our demonstrative pronouns ("this," "that," "these," "those"). See this article for more. 

of -- This word "of"  comes from the genitive case of the following word that requires the addition of a preposition in English.  The most common is the "of" of possession, but it can also mean "belonging to," "part of," "which is," "than" (in comparisons), or  "for," "concerning" or "about" with transitive verbs. 

the -- (WW) There is no Greek article "the" here in the source,. There is no indefinite article in Greek, but when a word doesn't have a definite article, the indefinite article can be added in English translation.

house  -- The word chosen here for "of the house" a less common form of the word for "house." Unlike the more common word, it isn't used to refer to a household, family, or clan, but the physical building, rooms, a meeting hall, property, and, specifically, to the ruling family of a nation. The last definition makes the most sense.

of -- (IW) There is nothing that can be translated as "of" in the Greek source.

Israel. -- The word translated as "Israel" comes from the Hebrew, not the Greek. The "destroyed of the ruling house of Israel is the house of David. David was, of course, a shepherd guiding the herd. It is not introduced by an article "the," so it is not "the house of Israel" but more simply "House Israel."