Jesus was first and foremost sent to the "lost sheep of Israel" but then he said he had "other sheep which were not of this fold, who would hear his voice" which pretty much started with the conversion of the Roman Centurion Cornelius by the Apostle Peter. Eventually they would become "one flock" with "one Shepherd".
I would like to expound on and clarify this understanding, dear Awen, if I may (as always, peace to you!). It is true that my Lord was sent to the lost sheep of Israel; however, Cornelius was one such sheep. The "little flock" were the Jews, which does not include the 10-tribe kingdom of Israel. Those... the "Samaritans"... were ALSO lost sheep of Israel. Along with non-Israelite nations, they make up "the nations" or "gentiles" (which is simply one who is not a Jew, and although from Israel, one from, say, the tribe of Simeon, is not a Jew. Jews hail from Judah and Benjamin).
The failure to understand just who "Israel" is (at least 10 tribes in ADDITION to the "Jews") is one of the reason many don't understand who the 144,000 seen by John are. It is why folks talk of "Israel" being exiled into Babylon... which is true, to a point. Since Jews (Judah and Benjamin) ARE Israel (the 2-tribe kingdom of Judah, with its capital city at Jerusalem, and Rehoboam as its king after Solomon), it's okay to say this; however, it sends the erroneous message that ALL of Israel (all 12 tribes) were exiled to Babylon, which isn't true. The 10-tribe kingdom of Israel (with its capital city at Bethel and Jeroboam as its king after Solomon) was exiled into Samaria by the Assyrians. Thus, the SAMARITANS... are ALSO the lost sheep of Israel.*
Which is why my Lord:
(1) not only spoke to the Samaritan woman at Jacob's well, but did not tell her (as he did the woman from Phoenecia), that it wasn't "right" to give HER the food of the little children - Israel. Because she WAS Israel, too, which is why she referenced the worship of their mutual forefathers when she said, "OUR forefathers used to worship in the mountain." She meant his and HER mutual forefathers... from Abraham to David (David transferred worship to Jerusalem when he took the Ark [of the Covenant] there)...
(2) told his disciples that they would be witnesses of him "in all Judea AND Samaria, and to the distant parts of the earth"... and
(3) the first person Peter was sent to was not a Jew, but a Samaritan: Cornelius. Cornelius lived in Caesarea, which is a city in Samaria.
Also, Cornelius wasn't a Roman Centurion; he was a member of the "Italian" band (which wasn't the Roman Army itself). Although Rome had conquered the Italian peninsula and required all of the cities conquered to send Rome taxes (and troops), some of the city-states were given certain rights. For instance, some were allowed full Roman citizenship (especially those nearest to Rome). Others were allowed certain Roman rights. Some, however, were allowed complete autonomy... although required to act as an ally, if and when needed. They maintained their own armies and it is in this light that Cornelius was an ITALIAN centurion, and not a ROMAN centurion. And it does make a difference as they were not the same thing.
For Cornelius to have been a ROMAN centurion would have made him worse than a tax collector as it was the Roman Army that was instrumental in putting my Lord to death. He, too, would have been used to put Israelites, Jews, and christians to death. Yet, he did not have the "status" that Saul of Tarsus, a Jew, did, such that that one was called to "suffer" for my Lord's name, as opposed to be called due to his prayers being heard, like Cornelius. Cornelius was not a Roman praying to the God of Israel - he was an Israelite (as was the Ethiopian eunuch) praying to the God of Israel. Where one is from (Samaria, Ethiopia, Galatia, etc.) does not exclude one from being an Israelite, any more than, say, being from American (vs. Israel) does.
So, as to the OP's question (peace to you, as well!) as to who my Lord was speaking of: he was speaking of gentiles... which includes Israel who were/are NOT Jews (i.e., the 10-tribe kingdom (of Israel))... and those of non-Israelite nations.
I hope this helps and, again, I wish you all peace!
Servant to the Household of God, Israel, and those who go with... and a slave of Christ,
SA