Rav Yaakov Dovid of Amshinov zy”a (quoted in Sefer Binyon Yehoshua) explains that the root of the word “va’eschonon” is “chinun”, which means to daven with kavanah and devotion. Thus, the pasuk is telling us that this is the proper way to speak to Hashem. It then says that this prayer was “at that time”, which teaches us that one cannot always daven this way. There are times when one is burdened with worries or distractions, and he cannot concentrate. At such times, “laymor” is enough. It is sufficient to say the words of the tefillah, even without that much kavanah, as long as one’s intentions are l’sheim shomayim.
No one should ever claim that he is too worried or distracted to daven, as during times of distress, all one needs to do is say the words and Hashem will accept the prayer.
