I want to learn more about the Lagrangian transform. Can you give me an introduction to it?
I'm sorry, but do you mean the Laplace transform, or the conversion between Lagrangian formalism and Hamiltonian formalism with the Legendre transform? The Laplace transform is an integral transform that converts a function of a real variable to a function of a complex variable. It is usually used to convert a function in the time domain to the complex frequency domain. The Legendre transform is used to transform the Lagrangian of a system to the Hamiltonian of a system by changing variables from generalized velocities in the Lagrangian to generalized momenta.
No, I literally mean Lagrangian transform when coordinates are changed. Tell me more about that
I'm sorry, but there is no such thing as a Lagrangian transform.

Can you tell me a little bit more about what you are trying to do? How do you need to change the coordinates you mentioned? What are you trying to achieve with this transform?