All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
The use of the Arabic word rabb without the definite article or in conjunction with another word does not render the word definite nor does it imply specifying or singling out an object from all the other objects of the same kind. However, the word Ar-Rabb (The Lord) with the definite article is used only in reference to Allaah. Ath-Thaʻaalibi wrote, "No created being should be referred to as Ar-Rabb with the definite article; rather, the word rabb without the definite article may be used in conjunction with another word, meaning the lord or master of such-and-such because only Allaah is the Lord and Master of all things..." [Tafseer Ath-Tha'aalibi]
Ar-Raazi wrote, "Ar-Rabb is one of the Names of Allaah Almighty and cannot be used in reference to other than Him except if it (the word rabb) used in conjunction with another word, in the genitive, without the definite article..." [Mukhtaar As-Sihaah]
The arabs did not use the word rabb without conjunction with another word except in reference to Allaah. Az-Zamakhshari wrote, "Scholars used the word Ar-Rabb with the definite article only in reference to Allaah. To refer to other than Him, it must be used in conjunction with another word, such as saying rabb ad-daar (owner of the house) or rabb ad-daabbah (owner of the animal)..."
Since the word Ar-Rabb is used with the definite article only in reference to Allaah, then it certainly indicates Tawheed.
However, if you mean the word rabb in conjunction with another word, then it is used in reference to other than Allaah as well, like in saying rabb ad-daar (owner of the house) or rabb ad-daabbah (owner of the animal). Ibn Faaris wrote, "The letters raa' and baa' (individual Arabic letters that make up the word 'rabb') make up the original root of the word; it conveys different meanings: the first is to reform a thing and look after it, so Ar-Rabb is the Owner, Creator, and Master who sustains and nurtures His creatures ... The rabb is the one who rectifies the affairs of something ..." [Muʻjam Maqayees Al-Lughah]
Allaah knows best.