Here's what I found (numbers are via Accordance):
אֵל ('el) occurs once
אֱלֹהִים ('elohim) doesn't occur at all!
But יְהוָה (YHWH) occurs 32 times
and אֲדֹנָי ('adonai) occurs 14 times (only Amos and Ezekiel have a higher percentage occurrence)
finally, עֶלְיוֹן occurs twice (only Psalms has a higher percentage occurrence)
Interesting, isn't it? Not quite sure what to make of it yet, but it does seem to reflect the personal nature of the laments. I wonder if there is any significance in the location of אֵל ('el) occurring in 3:41? And that it occurs as אֵל בַּשָּׁמָיִם ('el beshamayim)? The only other place that phrase occurs is Deut 3:24 where Moses is pleading with God to let him cross the Jordan:
Please, Lord God! You have only begun to show your servant your greatness and your mighty hand. What god in heaven or on earth can act as you do or can perform your deeds and powerful acts? (CEB)The phrase "God of Heaven"—as opposed to "God in Heaven"—occurs (as אֱלֹהֵי הַשָּׁמַיִם ['elohe hashamayim (Heb)][9 times] and as אֱלָהּ שְׁמַיָּא ['elah shemaya (Aram)] [12 times]) 22 times. I know, the numbers don't add up—there is a Hebrew occurrence of אֵל הַשָּׁמָיִם ('el hashamayim) in Psalm 136.
So, what do you make of all this?
By the way, אֱלֹהִים doesn't occur in Esther (but we all know that, right?) nor does it occur in the Song of Songs (no surprise there, either) or Obadiah, and it only occurs once in Nahum. Is there any significance that both Obadiah and Nahum are about the destruction of Edom and Babylon (respectively) and Lamentations is about the destruction of Jerusalem?
Food for thought, anyway...