The double reference to Jerusalem, following as it does the name of the city at the end of Luke 13:33, draws attention to it. It was the city of Jesus" destiny and the pathetic, unresponsive object of His love. Jesus" lament recalls Jeremiah"s lamentation over Jerusalem"s destruction by the Babylonians (cf. Jeremiah 12:7; Jeremiah 22:5; Lam.). The city was heading for a similar fate under the Romans for rejecting Jesus. The house left desolate is perhaps the temple (cf. 1 Kings 9:7-8), though this could be a reference to the nation as a whole, the city, or the Davidic dynasty. [source][source][source]
"The great expectations in the birth narrative for the redemption of Israel and Jerusalem are not being realized in the anticipated way and with the anticipated fullness, because Jerusalem is failing to recognize the time of its visitation. The great expectations aroused at the beginning contribute to the tragic effect of this turn in the plot, for we feel the loss more keenly in contrast to these great hopes." [1][source]
The city would not see Jesus until the Triumphal Entry ( Psalm 118:26; Matthew 21:1-9; Luke 19:28-38). However, the final and true fulfillment of the prophecy of the people of Jerusalem hailing the arrival of their Messiah is still future ( Matthew 23:39). Jesus gave two predictions of the fulfillment of Psalm 118:26. The one here was fulfilled at the Triumphal Entry. The second one that He gave after the Triumphal Entry ( Matthew 23:39) will be fulfilled at the Second Coming. [source][source][source]
Jesus" lament constituted a formal rejection of Israel for her rejection of her Messiah (cf. Matthew 23:37-39). Jesus used Jerusalem figuratively (i.e, in metonymy) for the whole nation. However, Jesus rejected her with a broken heart. He continued to offer Himself to the nation, but its fate was now irrevocable. [source][source][source]