This is not about the L(xM,N) lineages but about the Eurasian ones like R0a or R2.
Jeffrey I. Rose et al., Tabula rasa or refugia? Using genetic data to assess the peopling of Arabia. Arabian Archaeology and Epigraphy, 2013. Pay per view → LINK [doi:10.1111/aae.12017]
This paper provides a broad overview of the current state of archaeogenetic research in Arabia. We summarise recent studies of mitochondrial DNA and lactase persistence allele -13915*G in order to reconstruct the population histories of modern Arabs. These data, in turn, enable us to assess different scenarios for the peopling of the Peninsula over the course of the Late Pleistocene and Early Holocene. The evidence supports the posited existence of Arabian refugia, although it is inconclusive which (e.g. Persian Gulf basin, Yemeni highlands and/or Red Sea basin) was/were responsible for housing ancestral populations during the Last Glacial Maximum. Synthesising genetic and archaeological data sets, we conclude that a substantial portion of the present South Arabian gene pool derives from a deeply rooted population that underwent significant internal growth within Arabia some 12,000 years ago. At the same time, we interpret the disappearance of Nejd Leptolithic archaeological sites in southern Arabia around 8000 years ago to represent the termination of a significant component of the Pleistocene gene pool.
Rose uploaded the full paper at Academia.edu. Very much worth a careful read because it is a rare case of paleogenetics being done by a researcher who is primarily an archaeologist and who knows well the material Prehistory of which he's talking about, at all moments seeking to reconcile archaeological and genetic evidence and not, as way too often happens, creating genetic-only models with absolutely no material foundations and unavoidably clashing with prehistoric reality.