In pursuing net zero emissions amid increasing energy consumption, renewable energy sources offer a path towards environmental sustainability. However, they are plagued by instability and intermittency. Energy storage systems have emerged as a solution to address these challenges, ensuring a stable power supply despite the fluctuations of renewables. Liquid air energy storage (LAES) has advantages over compressed air energy storage (CAES) and Pumped Hydro Storage (PHS) in geographical flexibility and lower environmental impact for large-scale energy storage, making it a versatile and sustainable large-scale energy storage option. However, research on integrated closed Brayton cycle (CBC) systems with LAES is still in infancy. A novel integrated system is proposed, incorporating LAES, CBC and solar power. Steady-state models for LAES and CBC were developed and validated in Aspen Plus® V12. A comprehensive and systematic evaluation of the proposed LAES-CBC system was performed. The optimal round-trip efficiency (RTE) reaches up to 68.82 %, improving 11.70 % compared to the base LAES-CBC system. Parametric analysis reveals that higher compressor outlet pressures enhance both exergy efficiency and RTE. Compressors contribute significantly to exergy destruction, particularly in the charging process. The optimal outlet pressure for PUMP1 is found to be 80 bar. Economic analysis shows a reasonable payback period of 8.60 years and 0.307 $/kWh of LCOS, confirming the system's financial viability.