Possible to rename independent variable name in Built-in lmfit fitting models?
Sorry, I don't think that is possible.
I think you will have to rewrite the functions to use q instead of x.  That is, lmfit.Model uses function inspection to determine the names of the function arguments, and most of the built-in models really do require the first positional argument to be named x.
I am using lmfit to do small angle X-ray scattering pattern fitting. To this end, I use the Model class to wrap my functions and to make Composite Models which works well. However, it happened that I wrote all my function with 'q' as the independent variable (convention in the discipline).  Now I wanted to combine some of those q-functions with some of the built-in models. It clashes, because the independent_variable for those is 'x'. I have tried to do something like modelBGND = lmfit.models.ConstantModel(independent_vars=['q']), but it gives the error:

ValueError: Invalid independent variable name ('q') for function
  constant

Of course this can be solved, by either rewriting the built-in function again in 'q', or by recasting all my previously written functions in terms of 'x'. I am just curious to hear if there was a more straight forward approach?