Israel was to flee their captivity. When Isaiah wrote, it was an Assyrian captivity, not a Babylonian captivity. Isaiah chapters 48 and 49 are among those considered as having been written by Deutero-Isaiah and are dated to after the Babylonian captivity. The emphasis on Babylon is one of the reasons that they are so dated.
If these chapters were written after Lehi left Jerusalem, there is easy explanation for their presence. It is possible, however, that they originally dealt with the contemporaneous Assyrian captivity of the northern kingdom, or Israel. A later redactor may have updated them for what had to have been seen as a direct parallel. This explanation is, of course, entirely speculative.
In any case, by the time Nephi wrote this, his people had already fled from Laman and Lemuel’s murderous intentions, and Nephi would have seen that as a likening to fleeing Babylon.
The promise to Israel, and to the Nephites, was that Jehovah would lead them. Just has Jehovah protected Israel in their Exodus, he would continue to guide and care for them. Nephi had drawn his people’s story in pictures paralleling the Exodus, and certainly saw this promise being refocused on his people.
Unfortunately, the final verse indicates that Jehovah’s guidance would not provide permanent peace. Later in the Book of Mormon, it will be written several times that the Nephites had continual peace. Few of those continual peace periods lasted as long as three years, and some barely a year.