We present the discovery and preliminary characterisation of two high-redshift gravitationally lensed quasar systems in Gaia Data Release 2 (DR2). Candidates with multiple close-separation Gaia detections and quasar-like colours in WISE, Pan-STARRS, and DES are selected for follow-up spectroscopy with the New Technology Telescope. We confirm DLS J215028.71-465251.3 as a z = 4.130 +/- 0.006 asymmetric, doubly imaged lensed quasar system and model the lensing mass distribution as a singular isothermal sphere. The system has an Einstein radius of 1.202 +/- 0.005 arcsec and a predicted time delay of similar to 122.0 d between the quasar images, assuming a lensing galaxy redshift of z = 0.5, making this a priority system for future optical monitoring. We confirm PS J042913.17+142840.9 as a z = 3.866 +/- 0.003 four-image quasar system in a cusp configuration, lensed by two foreground galaxies. The system is well modelled using a singular isothermal ellipsoid for the primary lens and a singular isothermal sphere for the secondary lens with Einstein radii 0.704 +/- 0.006 and 0.241 +/- 0.030 arcsec, respectively. A maximum predicted time delay of 9.6 d is calculated, assuming lensing galaxy redshifts of z = 1.0. Furthermore, PS J042913.17+142840.9 exhibits a large flux ratio anomaly, up to a factor of 2.66 +/- 0.37 in i band, that varies across optical and near-infrared wavelengths. We discuss LSST and its implications for future high-redshift lens searches and outline an extension to the search using supervised machine learning techniques.