A Model Independent Universal Property for the Lax 2-Functor Classifier

In this article we provide a model-independent definition of the concept of lax $2$-functors from $(\mathrm{\infty },2)$-category theory and show that it agrees with the existing and widely used combinatorial model for those in terms of inert-cocartesian functors, which is utilized for example in the foundational work of Gaitsgory and Rozenblyum on Derived Algebraic Geometry to talk about the lax Gray tensor product.