The lithium cycling in the supra-subduction mantle wedge is crucial for understanding the generation of Li-rich magmas that may potentially source ore deposition in continental arcs. Here, we look from the mantle source perspective at the geological processes controlling the Li mobility in convergent margins, by characterizing a set of sub-arc mantle xenoliths from the southern Andes (Coyhaique, western Patagonia). The mineral trace element signatures and oxygen fugacity estimates (FMQ > + 3) in some of these peridotite xenoliths record the interaction with arc magmas enriched in fluid-mobile elements originally scavenged by slab dehydration. This subduction-related metasomatism was poorly effective on enhancing the Li inventory of the sub-arc lithospheric mantle, underpinning the inefficiency of slab-derived fluids on mobilizing Li through the mantle wedge. However, major and trace element compositions of mantle minerals in other xenoliths also record transient thermal and chemical anomalies associated with the percolation of slab window-related magmas, which exhibit an "adakite"-type geochemical fingerprint inherited by slab-derived melts produced during ridge subduction and slab window opening event. As these melts percolated through the shallow (7.2-16.8 kbar) and hot (952-1054 degrees C) lithospheric mantle wedge, they promoted the crystallization of metasomatic clinopyroxene having exceptionally high Li abundances (6-15 ppm). Numerical modeling shows that low degrees (< 10%) of partial melting of this Li-rich and fertile sub-arc lithospheric mantle generates primitive melts having two-fold Li enrichment (similar to 13 ppm) compared with average subduction-zone basalts. Prolonged fractional crystallization of these melts produces extremely Li-enriched silicic rocks, which may stoke the Li inventory of mineralizing fluids in the shallow crust.