I think it's not necessary to assume that the Steppe/EHG admixture came in relatively pure form to the Levant. If it arrives after the Bronze Age, the newcomers would have been admixed with non-Steppe populations. Likewise, it is not compulsory to believe that the Neolithic Levant and Chalcolithic Iran admixture of Bronze Age Levant is the same as the one found in modern Lebanese. Most people assume that modern populations inevitably inherit a big share of the DNA of previous inhabitants to the region. But that is not necessarily the case. If there are been a population in Iran or Mesopotamia that carried a similar mix of Neolithic Levant and Chalcolithic Iran, but also with Steppe/EHG, and that population replaced almost completely the BA Levant population during the Bronze Age, it would be invisible using those simple admixtures.
That's also how I feel. That paper is rather sloppy in its use of admixtures. Not even differentiations. If they don't even bother distinguishing Chalcolithic Iran from Neolithic Iran, or Neolithic Levant from Neolithic Anatolia, how could they ever know if the the population of modern Lebanon is really descended mostly from that of Bronze Age Lebanon? It could be that half or more of the green and orange admixture they reported in modern Lebanese came during the Iron Age (Sea Peoples, Greeks, Romans), or even during the Middle Ages with European crusaders. That would explain why there was such a strong rise in blue EHG/Steppe admixture. On the other hand it doesn't explain the complete lack of pink WHG admixture. So it's more likely that another population, perhaps from LBA or Iron Age Iran, already possessed a blend of blue, green and orange (without any pink), and replaced a big part of the earlier BA population in the Levant. It could have been the Persians, for instance.