Lithium depletion and enrichment in the cosmos is not yet well understood. To help tighten constraints on stellar and Galactic evolution models, we present the largest high-resolution analysis of Li abundances A(Li) to date, with results for over 100000 GALAH (Galactic Archeology with HERMES) field stars spanning effective temperatures 5900K≲Teff≲7000K and metallicities −3 ≲ [Fe/H] ≲ +0.5. We separated these stars into two groups, on the warm and cool sides of the so-called Li dip, a localized region of the Kiel diagram wherein lithium is severely depleted. We discovered that stars in these two groups show similar trends in the A(Li)–[Fe/H] plane, but with a roughly constant offset in A(Li) of 0.4dex⁠, the warm group having higher Li abundances. At [Fe/H]≳−0.5⁠, a significant increase in Li abundance with increasing metallicity is evident in both groups, signalling the onset of significant Galactic production. At lower metallicity, stars in the cool group sit on the Spite plateau, showing a reduced lithium of around 0.4dex relative to the primordial value predicted from big bang nucleosynthesis (BBN). However, stars in the warm group between [Fe/H] = −1.0 and −0.5 form an elevated plateau that is largely consistent with the BBN prediction. This may indicate that these stars in fact preserve the primordial Li produced in the early Universe.