The following is my chronologically-ordered list of events which took place in the Levant in 701 BC.
For Sennacherib’s Prism, see here.
Sennacherib conquers Phoenicia.
Sennacherib sends some of his army to Jerusalem by way of Beitin as in Isaiah 10:28-32, to corner Hezekiah in Jerusalem “like a bird in a cage”. Some fortifications (possibly siege-walls, NOT, as in one translation, earthworks; Assyrian “birati”, a word having a Hebrew equivalent of birah) were thrown up against Hezekiah just outside Jerusalem. No earthworks/siege ramps were erected against Jerusalem, as is clearly stated by Isaiah in 2 Kings 19:32.
Sennacherib conquers North Philistia, possibly with destruction of structures.
Sennacherib battles first Egypto-Nubian army; wins.
Sennacherib takes Eltekeh (probably with destruction of structures).
Sennacherib takes Timnah (definitely with destruction of structures).
Sennacherib may have possibly taken Azekah, and, therefore, have ravaged the Shephelah cities north of it at this point, if Ekron is the Philistine city mentioned in the Azekah inscription.
There is a small probability Sennacherib may have taken Gath at this point.
Sennacherib takes Ekron (definitely without destruction of structures) and ‘liberates’ it from the anti-Assyrian usurpers.
Sennacherib’s army probably ravages the Shephelah N. of the Elah Valley at this point, Sennacherib witnessing the conquests of Azekah and what is probably Gath.
The Assyrian army continues to ravage the Shephelah.
Sennacherib moves his army to Ashkelon and forces the city to submit.
Sennacherib begins the siege of Lachish.
The Tartan, Chief Cupbearer, and Chief Eunuch of Sennacherib are sent from Lachish to Jerusalem to demand Hezekiah’s surrender.
Sennacherib’s army attacks Rabud, Mirsim, ‘Aitun, Halif, and the Negev.
Sennacherib’s army destroys Lachish.
The Assyrian siege of Jerusalem is lifted.
Sennacherib moves to depopulate Libnah (in the Tel Goded-‘Erani/Beit Guvrin-Kiryat Gat area), so as to continue making the Shephelah an uncontested wilderness among the cities of Philistia and Judah.
Sennacherib hears of a second Egypto-Nubian attack (2 Kings 19:9a).
Sennacherib destroys Libnah and quickly departs to Assyria (2 Kings 19:7, 36).
The temporary territories of Judah from Aijalon to Tel Harasim and the permanent ones between Eshtaol and Azekah were given to Ekron. Gath was given to Ashdod (-Yam). Gaza received unknown territory in the W. Negev and to the S. of Lachish. North Philistia was given to Ekron.