Lord is the same noun of address used in verse 2. Although the term may mean Lord, in the present context it may best be understood as a noun of polite address (Good News Translation “Sir”). See comments at Matthew 8.2.
Servant (New American Bible “serving boy”) may mean either “servant” or “boy” (that is, “son”). The Lukan parallel initially has a word which specifically means “servant” (7.2), though in Luke 7.7 a shift is made to the same word which Matthew uses here. The only place in the New Testament where the word clearly means “son” is John 4.51. The plural form is used in Matthew 21.15, where it included both male and female children. The plural form is also used in 2.16, but there it may mean either “boys” or “children.” Here the word is probably used of the Roman officer’s orderly, which seems to be the understanding reflected in Bibel im heutigen Deutsch, 1st edition. Hence the translation can either be “my servant” or “the man who serves me.”
Lying paralyzed at home: Good News Translation, Bibel im heutigen Deutsch, 1st edition, and Bijbel in Gewone Taal further identify the place where he is lying … at home as “in bed.” The Greek text does not specify the nature of the paralysis, and it is best to select a very general term such as “unable to move” (Good News Translation).
As in Good News Translation, it is probably good to indicate that he is paralyzed because of some illness, as in “he is sick and unable to move at all” or “he has an illness which makes him so he can’t move. He is lying in bed at home.”
In terrible distress translates an adverb, terrible, plus a participle, in … distress; the verb form for distress is used in verse 29, where it is translated “to torment.” See also 14.24.
In terrible distress can be translated “he is suffering greatly,” “he is in great pain,” or “the pain is causing him great suffering.”
Quoted with permission from Newman, Barclay M. and Stine, Philip C. A Handbook on the Gospel of Matthew. (UBS Handbook Series). New York: UBS, 1988. For this and other handbooks for translators see here .