A gateless lateral p-n junction with reconfigurability is demonstrated on graphene by ion-locking using solid polymer electrolytes. Ions in the electrolytes are used to configure electric-double-layers (EDLs) that induce p- and n-type regions in graphene. These EDLs are locked in place by two different electrolytes with distinct mechanisms: (1) a polyethylene oxide (PEO)-based electrolyte, PEO:CsClO4, is locked by thermal quenching (i.e., operating temperature < Tg (glass transition temperature)), and (2) a custom-synthesized, doubly-polymerizable ionic liquid (DPIL) is locked by thermally triggered polymerization that enables room temperature operation. Both approaches are gateless because only the source/drain terminals are required to create the junction, and both show two current minima in the backgated transfer measurements, which is a signature of a graphene p-n junction. The PEO:CsClO4 gated p-n junction is reconfigured to n-p by resetting the device at room temperature, reprogramming, and cooling to T < Tg. These results show an alternate approach to locking EDLs on 2D devices and suggest a path forward to reconfigurable, gateless lateral p-n junctions with potential applications in polymorphic logic circuits.