In automotive suspension systems, the shock absorber plays a crucial role in decoupling the chassis from the wheel, making its design essential for achieving a good ride comfort. In addition to the damping force generated by hydraulic shock absorbers, the friction significantly contributes to the total force particularly at low relative velocities. For strut-type suspensions, fluctuating side forces considerably impact the normal loads of the friction contacts and thus the friction state. However, its dynamics under varying normal loads have not yet been thoroughly investigated and modelled, which is necessary to accurately analyse the effect of shock absorber friction in vehicle dynamics simulations. In this study, both stationary and non-stationary friction phenomena occurring in an automotive shock absorber are presented. The observances highlight the interdependent effect of relative velocity and normal force on the friction force. This requires new modelling approaches and is addressed by extending the LuGre formulation. The proposed formulation more accurately replicates the experimentally observed non-stationary behaviour over a wide variation of velocities and side forces during sine excitation. An iterative parameterisation process enables the incorporation of varying normal force effects on the Stribeck curve by expressing parameters as side-force dependent, which is new to the field. The enhanced friction model is validated using stochastic, real-driving shock absorber motion sequences, confirming a good agreement with the experimentally observed friction force. Based on this, a simplified heuristic approach is developed that further increases accuracy and is suitable for future suspension simulation. Eventually, a much higher accuracy can be achieved compared to state-of-the-art models.