No, the statement following confirms it: Her pursuers have all overtaken her in the midst of her distress
(Lamentations 1:3). This particular description of the event appears throughout (Lamentations 1:6, Lamentations 3:43, Lamentations 3:66, Lamentations 5:5). So although there were attempts at escape, they were unsuccessful. An example is provided in King Zedekiah’s failed attempt (see 2 Kings 25:1–7).
3 Judah has gone into exile because of affliction and hard servitude; she dwells now among the nations, but finds no resting place; her pursuers have all overtaken her in the midst of her distress.