In this work, we propose and investigate numerically the electronic transitions of a new system useful for quantum information tasks composed by a graphene quantum dot (GQD) interacting with two Li+ ions in opposed facing directions. By changing the distance of the Li+ ions, we find a region in which only electronic transitions of GQD -> Li+ are allowed. Notably, into this region emerges the possibility of controlled electronic transitions for both ions in the symmetric case via appropriate external electric fields. Finally, the robust entanglement generation arises since it is possible to inhibit the electronic transition back to GQD by grounding it.