The Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) is an untargeted spectroscopic survey that aims to measure the expansion rate of the Universe at $z ∼ 2.4$ to 1% precision for both $H(z)$ and $D_A(z)$. HETDEX is in the process of mapping in excess of one million Lyman Alpha emitting (LAE) galaxies and a similar number of lower-z galaxies as a tracer of the large-scale structure. The success of the measurement is predicated on the post-observation separation of galaxies with Ly$α$ emission from the lower-$z$ interloping galaxies, primarily [OII], with low contamination and high recovery rates. The Emission Line eXplorer (ELiXer) is the principal classification tool for HETDEX, providing a tunable balance between contamination and completeness as dictated by science needs. By combining multiple selection criteria, ELiXer improves upon the 20 Angstrom rest-frame equivalent width cut commonly used to distinguish LAEs from lower-$z$ [OII] emitting galaxies. Despite a spectral resolving power, R $∼800$, that cannot resolve the [OII] doublet, we demonstrate the ability to distinguish LAEs from foreground galaxies with 98.1% accuracy. We estimate a contamination rate of Ly$α$ by [OII] of 1.2% and a Ly$α$ recovery rate of 99.1% using the default ELiXer configuration. These rates meet the HETDEX science requirements.