We present XMM-Newton X-ray observations of nine confirmed lensed quasars at 1 ≲ z ≲ 3 identified by the Gaia Gravitational Lens program. Eight systems are strongly detected, with 0.3-8.0 keV fluxes F 0.3-8.0 ≳ 5 ×10-14 erg cm-2 s-1. Modeling the X-ray spectra with an absorbed power law, we derive power-law photon indices and 2-10 keV luminosities for the eight detected quasars. In addition to presenting sample properties for larger quasar population studies and for use in planning for future caustic-crossing events, we also identify three quasars of interest: a quasar that shows evidence of flux variability from previous ROSAT observations, the most closely separated individual lensed sources resolved by XMM-Newton, and one of the X-ray brightest quasars known at z > 3. These sources represent the tip of the discoveries that will be enabled by SRG/eROSITA.