  We report synthesis, ^{195}Pt, ^{11}B and ^{7}Li NMR measurements, and
first-principle band calculation for non-centrosymmetric superconductors
Li_{2}(Pd_{1-x}Pt_{x})_{3}B (x=0, 0.2, 0.5, 0.8, 0.84, 0.9 and 1). For 0 \leq x
\leq 0.8, the spin-lattice relaxation rate 1/T_1 shows a clear coherence peak
just below T_c, decreasing exponentially at low temperature, and the Knight
shift ^{195}K decreases below T_c. For x=0.9 and 1.0, in contrast, 1/T_1 shows
no coherence peak but a T^3 variation and ^{195}K remains unchanged across T_c.
These results indicate that the superconducting state changes drastically from
a spin-singlet dominant to a spin-triplet dominant state at x=0.8. We find that
the distortion of B(Pt,Pd)_6 increases abruptly above x=0.8, which leads to an
abrupt enhancement of the asymmetric spin-orbit coupling as confirmed by band
calculation. Such local structure distortion that enhances the extent of
inversion-symmetry breaking is primarily responsible for the pairing symmetry
evolution. The insight obtained here provides a new guideline for searching new
NCS superconductors with large spin-triplet component.
