To whom is the writer referring in these verses?

There are different opinions about whom the writer is referring to. The following are the main suggestions:

1. Some are of the opinion that the writer is referring to his own personal disaster. It is reasoned that there is no thought of a general application of the people suffering because the writer refers explicitly to my enemies. It is asserted that they cannot be the people’s enemies in general, but must indeed mean specific, personal opponents. These enemies are referred to as those who were my enemies without cause. The writer expresses his awareness that he has given no reason for their hostile action (see also Psalm 7:5; Psalm 35:19; Psalm 69:5). These enemies are seen as fellow citizens, although it is not clear from this lament what exactly their unlawful treatment consisted of.¹

2. Others are of the opinion that it is a description of the personal sufferings of Jeremiah. He had enemies without a reason (see Jeremiah 17:16; Jeremiah 18:20). He was also put in a pit to die (see Jeremiah 38:6). He also prayed for vengeance on his enemies (see Jeremiah 11:20; Jeremiah 12:3; Jeremiah 5:15; Jeremiah 17:18; Jeremiah 18:21–22; Jeremiah 20:12). If this is the case, it is argued as one of the reasons that Jeremiah is the writer of Lamentations.² The problem, however, is that there is nothing mentioned or known of his enemies having stoned him or of having covered him over with a stone after they had put him into the pit. In this context, the symbolic language should be considered. Different portions of what is described here are quoted from similar passages in the Psalms, whose figurative character is universally acknowledged.³ 

3. Another opinion is that the writer refers to the godly Israelites who suffered immensely when the kingdom with Jerusalem was destroyed. It may then refer not only to the destruction by the Babylonians but also suffering inflicted by their godless fellow-countrymen.  If this is the case, the writer then refers to the sufferings that had come on him and all the god-fearing people of God who were also struck by the circumstances.⁴

With all the above in mind, it is best to understand that the writer personifies the suffering of the lamenting nation while he identifies with them in it and expresses it as the misery of an individual. (See note elsewhere, regarding the identity of the writer, he is Jeremiah or someone else.)