This study emphasises the criticality of delay as a performance metric for signalized intersections and the challenges associated with its estimation, particularly in the context of Multi-class and Lane-free (MCLF) traffic conditions. Traditional delay models are often inadequate for such conditions, necessitating the development of a tailored approach. A novel delay equation is proposed, integrating insights from queuing theory principles with consideration of multi-class of vehicles and lane-free movement. Key features include assumption of random arrival and departure pattern as well as distribution, incorporation of Passenger Car Equivalent (PCE) and virtual lane concepts to account for the diverse vehicle classes and lane-free movement prevalent in Indian traffic. The model's efficacy is demonstrated through comparison with conventional in practice delay models, showing its superior performance. This tailored approach enhances the accuracy of delay estimation and also highlights the importance of accounting for specific traffic characteristics in optimising signal design for intersections under MCLF traffic conditions.