The electron-lattice interaction of BaPb1-xBixO 3 (BPB) and BaxK1-xBiO3 (BKB) is studied microscopically by using the realistic electronic bands of BaBiO 3 reproduced by the tight-binding model. It is found that the electron-lattice coupling coefficients have strong wavevector and mode dependences. The electron-lattice interaction causes a remarkable renormalization of the longitudinal oxygen stretching and/or breathing mode vibration. Superconductivity is discussed in the framework of the strong-coupling theory of the phonon mechanism. The spectral function alpha 2F( omega ) has some prominent structures in the frequency range of the oxygen stretching/breathing mode. As x increases, some of the main peaks in alpha 2F( omega ) shift to the lower-frequency side, reflecting the phonon frequency renormalisation. The transition temperature Tc and the energy gap function Delta ( epsilon ) at T=0 K have been evaluated by solving the Eliashberg equations. The calculated Tc increases rapidly with increasing x, and reaches about 30 K for x=0.7. The oxygen isotope shift of Tc in BKB is calculated and the characteristic exponent alpha defined by Tc varies as MOalpha (MO is oxygen atomic mass) is evaluated to be 0.35-0.45. The superconducting energy gap Delta 0 is evaluated to be 4.8 meV for x=0.7. The ratio 2 Delta 0/kBTc is found to have a value close to that predicted by the Bardeen-Cooper-Schrieffer weak-coupling theory (2 Delta 0/kBTc=3.5). However, the calculated tunnelling differential conductance dI/dV and its derivative d2I/dV2 show behaviours that are characteristic to the strong-coupling superconductor.