We report experimental evidence that indicated the lifting of the spin degeneracy of the two-dimensional (2D) electron ground subband due to the lack of inversion symmetry in narrow InAs/GaSb quantum wells. Through detailed analysis of the beating patterns in 2D electron Shubnikove"de Haas (SdH) oscillations, we conclude that the finite spin splitting at B=0 is dominated by the lack of inversion symmetry in the confining potential well. The effects of the inversion asymmetry connected with the InAs bulk structure, although they exist, are of minor importance in the samples studied. The 2D energy band structure in such asymmetric wells can be described by including the Rashba term, Hs.o.=+s(×k)z, into the electron Hamiltonian; the spin-orbit coupling constant +s=0.9×10-9 eV cm is determined for a 75- well by simulating the measured SdH oscillations. We also studied the magnetic field dependence of the spin splitting by rotating the sample in constant magnetic fields as high as 15 teslas. The results indicate that the spin splitting increases nonlinearly with the external magnetic field. Finally, the electron scattering times of the two spin states of the ground electron subband are not always the same; their difference is found to increase with the spin splitting. The possibility of spin-dependent scattering mechanisms is also discussed. © 1990 The American Physical Society.