The spin-orbit (SO) coupling parameters for the lowest conduction subband due to structural inversion asymmetry (SIA) and bulk inversion asymmetry (BIA) are calculated for a range of carrier densities in [001]-grown delta-doped n-type InSb/In1-xAlxSb quantum wells using the established eight-band k center dot p formalism [J. Deng , Phys. Rev. B 59, R5312 (1999)]. We present calculations for conditions of zero bias at 10 K. It is shown that both the SIA and BIA parameters scale approximately linearly with carrier density, and exhibit a marked dependence on well width when alloy composition is adjusted to allow maximum upper barrier height for a given well width. In contrast to other material systems, the BIA contribution to spin splitting is found to be of significant and comparable value to the SIA mechanism in these structures. We calculate the spin lifetime tau(s[1 (1) over bar0]) for spins oriented along [1 (1) over bar0] based on D'yakonov-Perel' mechanism using both the theory of Averkiev [J. Phys.: Condens. Matter 14, R271 (2002)] and also directly the rate of precession of spins about the effective magnetic field, taking into account all three SO couplings, which show good agreement. tau(s[1 (1) over bar0]) is largest in the narrowest wells over the range of moderate carrier densities considered, which is attributed to the reduced magnitude of the k-cubic BIA parameter in narrow wells. The inherently large BIA induced SO coupling in these systems is shown to have considerable effect on tau(s[1 (1) over bar0]), which exhibits significant reduction in the maximum spin lifetime compared to previous studies that consider systems with relatively weak BIA induced SO coupling. The relaxation rate of spins oriented in the [001] direction is found to be dominated by the k-linear SIA and BIA coupling parameters and at least an order of magnitude greater than in the [1 (1) over bar0] direction.