Identifying and characterizing young stars in the Solar neighbourhood is essential to find and describe planets in the early stages of their evolution. This work seeks to identify nearby young stars showing a lithium 6708{AA} absorption line in the GALAH survey. A robust, data-driven approach is used to search for corresponding templates in the pool of 434215 measured dwarf spectra in the survey. It enables a model-free search for best-matching spectral templates for all stars, including M dwarfs with strong molecular absorption bands. 3147 stars have been found to have measurable lithium: 1408G and 892 K0-K5 dwarfs (EW(Li)>0.1{AA}), 335 K5-K9 (>0.07{AA}) and 512 M0-M4 dwarfs (>0.05{AA}). Stars with such lithium features are used to investigate the possibility of searching for young stars above the main sequence based merely on their parallaxes and broad-band photometry. The selection of young stars above the main sequence is highly effective for M dwarfs, moderately effective for K dwarfs and ineffective for G dwarfs. Using a combination of the lithium information and the complete 6D kinematics from Gaia and GALAH, 305 new candidate moving group members have been found, 123 of which belong to the Scorpius-Centaurus association, 36 to the Pleiades and 25 to the Hyades clusters.