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Recent observational and theoretical results have suggested that some of ultraluminous X-ray (ULX) sources may contain neutron star (NS) accretors. However, the formation channel and properties of donor stars of NS ULXs remain uncertain. By adopting the non-conservative and rotation-dependent mass transfer model in the primordial binary evolution, we investigate the way to form pulsar ULXs like observed pulsar ULXs in a systematic way. Our simulation results indicate that pulsar ULXs with Be stars and intermediate or/and high mass donors match observed apparent luminosities, orbital periods and observationally indicated donor masses of known pulsar ULXs. ULXs with Be and intermediate donors are main contributors. The route of accretion-induced collapse of WDs has 4.5% contribution to the NS ULXs, 4.0% of NSs in ULXs are formed through electron-capture supernovae (SNe), and 91.5% of NSs in ULXs are born with core-collapse SNe. We also studied the evolution of pulsar ULXs to double compact star systems. We do not find NS-black hole systems (merging in a Hubble time) that evolved from pulsar ULXs. Pulsar-white dwarf (WD) cases that evolve through pulsar ULXs have significant contributions to the whole NS-WD gravitational wave sources. Contributions of pulsar-WD and pulsar-NS cases that experienced pulsar ULXs are $\sim$40% and 11% among all LISA NS-WD and NS-NS sources, respectively. Monte Carlo simulation noise with different models give a non-negligible uncertainty.