I disagree with Jeffro, in regards to what the writer of the book called "According to Luke" means by when the when "times of the Gentiles are fulfilled". For simplicity, in the rest of this post I will refer to the writer of the book as 'Luke', though the writer is actually anonymous.
Luke 21:24 (NASB) says "and they will fall by the edge of the sword, and will be led captive into all the nations; and Jerusalem will be trampled underfoot by the Gentiles until the times of the Gentiles are fulfilled." The Roman empire took many Jews as captives and did place them into various nations which were under Roman control, but the trampling of Jerusalem by gentiles didn't permanently end in 70 CE. [Furthermore, the trampling by gentiles began when the Babylonians conquered Jerusalem.] Note that the latter part of verse 24 uses the plural word of "Gentiles" and it used it twice. The verse does not say "a Gentile nation" will trample upon Jerusalem, but rather "Gentiles" (possibly meaning multiple gentile nations). Perhaps by "Gentiles" it simply means multiple gentile individuals (such as in the composition of the Roman armies), but it also speaks the trampling continuing until the times of the Gentiles end (are "are fulfilled").
Though the Romans destroyed Jerusalem in 70 CE, the trampling of Jerusalem by Gentile armies did not come to a permanent end then. Furthermore, the writer of the Gospel likely knew such, for the the gospel account was likely written well after the year 100 CE (possibly even after the Bar Kokhba revolt ended in the year 135 [or 136] CE). For example consider the following. The Jews, led by Bar Kokhba, had another revolt in Judah (after Masada fell in 71 CE to the Romans) and they temporarily liberated much of Judea (even Jerusalem) from the Romans, but the Romans armies eventually reconquered what they lost in Judea (including Jerusalem). See https://en.wikipedia.org/wiki/Bar_Kokhba_revolt . It says the following.
"Fought c. 132–136 CE,[6] it was the last of three major Jewish–Roman wars, so it is also known as the Third Jewish–Roman War or, the Third Jewish Revolt. Some historians also refer to it as the Second Revolt[7] of Judea, not counting the Kitos War (115–117 CE), which had only marginally been fought in Judea.
... Despite arrival of significant Roman reinforcements from Syria, Egypt, and Arabia, initial rebel victories established an independent state over most parts of the province for over three years, as Bar Kokhba took the title of Nasi ("head of state"). Many Jews regarded him as the Messiah, who would restore their national independence.[13]
... The Bar Kokhba revolt resulted in the extensive depopulation of the Jewish communities of Judea, more so than during the First Jewish–Roman War.[15] Some scholars describe it as a genocide.[15][16]
The Bar Kokhba revolt greatly influenced the course of Jewish history and the philosophy of the Jewish religion. Despite easing the persecution of Jews following Hadrian's death in 138 CE, the Romans barred Jews from Jerusalem, except for attendance in Tisha B'Av. Jewish messianism was abstracted and spiritualized, and rabbinical political thought became deeply cautious and conservative. .. It was also among the key events to differentiate Christianity as a religion distinct from Judaism.[22] Although Jewish Christians regarded Jesus as the Messiah and did not support Bar Kokhba,[23] they were barred from Jerusalem along with the other Jews.[24] "
Note the Wikipedia article says "It was also among the key events to differentiate Christianity as a religion distinct from Judaism". It is a significant point and it might indicate the gospel of 'Luke' was written after the Bar Kokhba revolt (or give us clues to the thinking of the writer of the gospel named after 'Luke'). Also keep in mind that 'Luke' was likely a gentile Christian instead of a Jewish Torah-keeping Christian.
Note that the Wikipedia source says it lasted from about (c.) 132 CE - 136 CE, however according to https://www.britannica.com/event/Bar-Kokhba-Revolt it lasted from 132 CE to 135 CE, for that source says the following.
"Bar Kokhba Revolt, also called Second Jewish Revolt, (132–135 ce), Jewish rebellion against Roman rule in Judaea.
... With the fall of Jerusalem
and then Bethar, the fortress to the southwest of Jerusalem where Bar
Kokhba was slain, the rebellion was crushed in 135. According to
Christian sources, Jews were thenceforth forbidden to enter Jerusalem."
The Jewish site at https://www.jewishvirtuallibrary.org/the-bar-kokhba-revolt-132-135-ce also says the war was from 132 CE to 135 CE. So which year did it end in, 135 CE or 136 CE? Did the war last for about 3.5 years?
The previously mentioned Jewish site says the following.
"In 135 C.E., Hadrian’s army besieged Bethar and on the 9th of Av, the Jewish fast day commemorating the destruction of the first and second Holy Temples, the walls of Bethar fell. After a fierce battle, every Jew in Bethar was killed. Six days passed before the Romans allowed the Jews to bury their dead.
Following the battle of Bethar, there were a few small skirmishes in the Judean Desert Caves, but the war was essentially over and Judean independence was lost. The Romans plowed Jerusalem with a yoke of oxen. Jews were sold into slavery and many were transported to Egypt. Judean settlements were not rebuilt. Jerusalem was turned into a pagan city called Aelia Capitolina and the Jews were forbidden to live there. They were permitted to enter only on the 9th of Av to mourn their losses in the revolt. Hadrian changed the country’s name from Judea to Syria Palestina."
Note that in 135 CE Jews were taken captive by Roman armies and sold into slavery and that many of them were taken to Egypt (a gentile nation) - and thus taken into captivity. That is very significant since Luke 21:24 says "will be led captive into all the nations; and Jerusalem will be trampled underfoot by the Gentiles until the times of the Gentiles are fulfilled". Thus from 132 CE to 135 CE (or possibly even to 136 CE) the Romans (a force made of up of gentiles) trampled Jerusalem under their feet. Note that after the war ended in 135 CE (or 136 CE) that Jerusalem was turned into a pagan city, with no Jews being allowed to live there. Surely for decades after 136 CE Jerusalem was thus being trampled by gentiles and under gentile control and thus the times of gentile rule upon Jerusalem was still in progress. I think it is very possible that 'Luke' (the writer of the gospel named after Luke, regardless of whom the actual writer was), wrote the gospel after the year 132 CE. Over about the next 1800 years (after 136 CE) various gentile nations took control of Jerusalem. West Jerusalem continued to be under gentile control until Jews conquered it in 1948, and East Jerusalem continued to be under gentile control until Jews conquered it in 1967. The times of gentile control over Jerusalem finally ended in 1967, though Israel allows gentile (Arab/Palestinian) citizens of Israel to be part of the government of Israel, and though Israel might make a peace treaty in which East Jerusalem (or some suburbs of it) becomes part of an independent Palestinian state recognized by both Israel and the U.S.A.