Advances of electron storage rings to beam currents of above 1 A and tabletop sizes make possible the development of a synchrotron-based source for EUV lithography (EUVL) at ~13.5-nm wavelength. The MIRRORCLE storage rings can provide on average 3-A electron beam current, 1-min lifetime, 15-ms radiation damping, and beam size ~3*3 mm2. MIRRORCLE-20SX, MIRRORCLE-6X, and MIRRORCLE-CV4 store electrons with energies of 20 MeV, 6 MeV, and 4 MeV, respectively. These machines can emit EUV from a tiny target, hit by the circulating beam, via transition radiation or diffusive radiation. Using a multilayer microelectromechanical system (MEMS) target allows enhancement and spectral purification of the emitted EUV. Aligning many such MEMS along the electron beam orbit and radiation collection by only one quasi-elliptical EUV mirror can provide EUV satisfying the joint requirements for an EUVL source.