Aside from the dreadful phrasing of the NWT version, it also problematically asserts that "good things" do not go forth from Jehovah as well. It is actually worse....BOTH "bad things" and "what is good" do not proceed from him, so in effect NOTHING proceeds from him. Instead, the context mentions actual examples of "bad things" that Jehovah has caused: Jehovah has "torn down the fortified places" (2:2), devours like a flame all those in Jacob (2:3), "become like an enemy" (2:5), "treats his booth violently" (2:6), "cast off his altar" (2:7), "causes the rampart and wall to go mourning" (2:8), "done what he had in mind" (2:17), "causes the enemy to rejoice" (2:17), "killed in the day of your anger" (2:21), "slaughtered without compassion" (2:21), "worn away my skin and broken my bones" (3:4), "hampers my prayer" (3:8), "is like a bear lying in wait" (3:10), "shot arrows into my kidneys" (3:13), "saturated me with wormwood" (3:15), etc. Then the author meditates on God's kindness and forgiveness and lists examples of "good things" that Jehovah brings: "acts of loving-kindness" (3:22), "mercies" (3:22), "good to the one hoping in him" (3:25), "good to the one waiting silently" (3:26), "not keep casting off forever" (3:21), "abundance of his loving-kindness" (3:32), "not approved subverting a man's cause" (3:36), etc. So it is clear in the overall context that the author means that Jehovah brings both "good" and "bad" things, or calamities.
The immediately preceding verse is also crucial: "Who is able to say ('mr) a thing, and have it come to pass, if it has not been commanded (tswh) by the Lord?" (3:37). The next verse then mentions both bad and good things going forth from "the mouth (mpy) of the Most High". The NWT rendering makes no sense in light of the preceding verse: v. 37 claims rhetorically that the only things that "come to pass" are those commanded by Jehovah, and v. 38 would then contradict this by saying that in fact good and bad things DO NOT proceed as utterances from his mouth. Instead, v. 38 would continue the thought in v. 37, that good and bad things DO proceed as utterances from his mouth, because things that "come to pass" have been "commanded by the Lord". So, this shows the importance of context!
Finally, there is the symmetry in that all three of the verses under Mem (in the acrostic) would posit rhetorical questions on the same theme.
On edit: See also Amos 3:6 which is quite appropriate to the theme of Lamentations (Jerusalem's destruction): "Does disaster befall a city, unless Yahweh has done it?"