From my understanding and experience
i) you cannot mix Lennard-Jones and Buckingham, you have to pick one of the two
ii) since at least GROMACS 2020 the Buckingham potential is not supported anymore (it is not stated in the manual)
One way to go is to fit the potential terms of your Buckingham in terms of a LJ potential and write a “pure” LJ potential. The quality of this approximation largely relies on the quality of the fits, I would say, I have no idea if this is a good approach. The other is to use tabulated potentials. Also this functionality is deprecated, and you will have to rely on older GROMACS versions (2019 being the newest still supporting the tabulated potential). Take a look at this.