The paper discusses and compares the Lambertian limits for light trapping (LT) in GaAs active layer based thin film solar cells as described by different mathematical theories and expressions. The Lambertian limits for thin film GaAs solar cell provide the maximum efficiency that can be achieved through LT structures and also indicate the advantage that these structure can provide for the design of GaAs thin film solar cell structure. The purpose to discuss difference Lambertian limit expressions is to understand and predict, which limiting benchmark value is more suited for nano LT structures based GaAs active material solar cells, considering GaAs material properties. The paper also compares these calculated limiting values with different nano LT structures including photonic crystal structures based designs proposed by the author. The aim is to check how much close a particular proposed structure is to the Lambertian values, so that we can predict that which is more suitable design to get best efficiency out of the single junction GaAs material based structure. The paper discussed the three Lambertian theories including that of Yablonovitch, Green and Schuster.