  In a binary, when the orbital plane of the companion star is almost edge-on
along the line-of-sight direction, this would produce an observable
self-gravitational lensing effect, which would slightly increase the overall
optical intensity of the binary. However, the probability of getting one
observable self-lensing binary (SLB) is very low. There are only five observed
SLBs so far and all of them are eclipsing binaries. In this article, we
theoretically show that the neutron star-white dwarf (NS-WD) binary PSR
J1910-5959A could be an observable non-eclipsing SLB. It might be the first
binary showing both periodic optical amplification and Shapiro time delay of
radio signals, which is useful to verify our understanding about gravitational
lensing in relativistic binaries. Moreover, we show that the observed peak
amplification limit of the PSR J1910-5959A can help constrain the radius of the
WD, which is a crucial parameter to examine the mass-radius and
temperature-radius relationship for helium WD.
