This verse uses the same vocabulary is a very similar way to Luke 15:24 when the father makes the statement about his son. In the Greek, the first part of this verse appears in the previous verse, Luke 15:31, but we cover it here. 

The Greek verb translated as "it was meet" is a special verb that means  "it is needful," and "there is a need." It is always singular referring to a specific moment in the past, present, or future. It works something like our word "must" but its form is fixed. 

The Greek verb translated as  "that we should make merry" means "cheer", "gladden", and in the passive, "make merry", "enjoy oneself". Used commonly in parables by Luke, specifically in the parable of the prodigal son. It is also used in the parable of Lazarus and the man building the warehouse. These three parables have a lot of uncommon features for Jesus's parables and this word is one of them.  It is in the form of a passive infinitive. In 15:24, it was an infinitive, but the subject acted on themselves. There the infinitive ended the sentence instead of beginning it as it does here. 

An untranslated Greek word appears here that means "but", "however", and "on the other hand". Since it always falls in the second position, translating it as "however" often captures its feeling better. 

The Greek word translated as "and" is used as the conjunction "and", but it also is used to add emphasis ("also").

The Greek verb translated as "be glad" means "rejoice", "take pleasure in," and "welcome." Again, the form is a passive infinitive, "to be enjoyed." This word is usually translated as "rejoice" but that doesn't work in the passive. 

The word translated as "for" introduces a statement of fact or cause, "because" in English.

"This" is translated from a Greek word that means "this", "that", "the nearer." 

The word translated as "thy" is the possessive form of the second person pronoun.

The word translated as "brother" means a biological brother, any kinsmen, and more broadly and friend or associate.

The verb "was" here is the common form of "to be" in Greek. It means to have a certain characteristic or remain in a certain condition. It also equates terms or assigns characteristics.

The word translated as "dead" acts as both a noun and an adjective. It  means "corpse", "a dying man," and "inanimate, non-organic matter." Christ uses it in all three senses, referring to the actual dead, the spiritually dead, and inanimate matter.

The Greek word translated as "and" is used as the conjunction "and", but it also is used to add emphasis ("also").

"Is alive again" is a Greek verb Jesus only uses here and in Luke 15:24. It  means to "return to life" and "be alive again."

The Greek word translated as "and" is used as the conjunction "and", but it also is used to add emphasis ("also").

The word translated as "was lost" means to destroy or demolish. It can also mean "to lose."  Jesus often uses it as the opposite of "found" so "lost". It is the form of an adjective, "having lost".

The Greek word translated as "and" is used as the conjunction "and", but it also is used to add emphasis ("also").

The term used for "is found" is the source of our word, "heuristic," meaning enabling a person to find out something for themselves. It means "find out" and "discover."