The low earth orbit (LEO) satellite system is one of the promising solutions to provide broadband services to a wide-coverage area for future integrated LEO-6G networks, where users' demands vary with time and geographical locations. Conventional satellites with fixed beam pattern and footprint planning may not be capable of meeting such dynamic requests and irregular traffic distributions. As the development of flexible satellite payload with beamforming capabilities, spot beams with flexible size and shape are considered potential solutions to this issue. As an early investigation, in this paper, we consider the scenarios where satellite payloads are equipped with multiple beam patterns and study the optimal beam pattern selection. We exploit the potential synergies of joint resource optimization between adaptive beam patterns and non-orthogonal multiple access (NOMA) in a LEO satellite system, where NOMA is employed to reduce intra-beam interference and flexible beam pattern is adopted to mitigate inter-satellite interference. The formulated problem is to minimize the capacity-demand gap of terminals, which falls into mixed-integer nonconvex pro-gramming (MINCP). To tackle the discrete variables and non-convexity, we design a joint approach to allocate power and select beam patterns. Numerical results show that the proposed scheme achieves capacity-demand gap reduction of 37.8% over conventional orthogonal multiple access (OMA) and 42.5% over the fixed-beam-pattern scheme.