The first major archaeological excavation at Tell ed-Duweir (= Tel Lachish) was called the Wellcome-Marston Archaeological Research Expedition, directed by James Leslie Starkey. During that expedition, in 1935 eighteen pieces of broken pottery with writing were found in a room outside the city gate. Three more pieces were found in 1938. J. A. Thompson explains the importance of the letters:
They represent correspondence between the military commander of Lachish, a certain Yoash, and outpost commanders, in the days when Nebuchadnezzar was closing in on Jerusalem. Most of these letters are poorly preserved, but six of them give useful information about the time. (The New International Dictionary of Biblical Archaeology)
Jerusalem was destroyed by the Babylonians in 586 B.C. These letters were written shortly before that time and were in the room at the time of the destruction of Lachish. Take a look at the biblical evidence. The prophet Jeremiah describes a time when only the Judean cities of Lachish and Azekah were left.
when the army of the king of Babylon was fighting against Jerusalem and against all the cities of Judah that were left, Lachish and Azekah, for these were the only fortified cities of Judah that remained. (Jeremiah 34:7 ESV)
Lachish Letter #4 indicates that only Lachish was left at the time of writing.
“And let (my lord) know that we are watching for *[fire] signals of Lachish, according to all the indications which my lord hath given, for we cannot see Azekah” (Pritchard, The Ancient Near East).
Letter #3 mentions a prophet.
And as for the letter of Tobiah, servant of the king, which came to Shallum son of Jaddua through the prophet, saying, ‘Beware!, thy servant hath sent it to my lord. (Pritchard, The Ancient Near East)
D. Winton Thomas says that this is “the first occurrence in non-Biblical texts of the common Hebrew word for prophet (nabi).”
The prophet Jeremiah may not be the prophet mentioned in Letter #3, but he was a prophet in Judah at the same time, and he wrote about the same situation. Notice Jeremiah 34:6-7 again.
Then Jeremiah the prophet spoke all these words to Zedekiah king of Judah, in Jerusalem, when the army of the king of Babylon was fighting against Jerusalem and against all the cities of Judah that were left, Lachish and Azekah, for these were the only fortified cities of Judah that remained. (Jeremiah 34:6-7 ESV)
This example provides wonderful corroborating evidence for the historical trustworthiness of the writing of Jeremiah.