The next step is to remove the dying branches of the house of Israel. At the time of Zenos, this would have been a direct reference to the Assyrian invasion that took away the top, or more importantly, the population of the kingdom of Israel. They were literally plucked off and were taken away. The idea that they were burned in the fire might simply suggest the scattering. The kingdom of Israel was effectively destroyed, but the people were not.
The young and tender branches were those that had heeded the prophets call for repentance. These were taken away. It is possible that since Zenos is seeing this prophecy from the perspective of the northern kingdom, some of the young branches were carried away to Jerusalem. Many were among those who were scattered among the ten tribes. The allegory suggests that there would be righteous among those scattered, who would later be gathered.
As Jacob tells the allegory, he clearly adds his own perspective, seeing the Babylonian invasion as doing the very same thing, and the descendants of Lehi were one of the young and tender branches that were taken away.