I just want to know whether Particle based rRESPA is possible or not in LAMMPS where I have mixture of heavy particle and light particle. The heavy particles will be integrated with longer timestep and light particle will be integrated with smaller timestep.
Yes, it is possible assuming the heavier particles have different atom types than the lighter particles and the mass difference is significant.
There is a misconception here about how r-RESPA functions. With r-RESPA the integration of the equations of motion is always done on the innermost, shortest timestep. What differs between r-RESPA levels is whether forces for a r-RESPA level are computed in a step or whether cached copies are used. The time spent on time integration to propagate atoms is very minimal in comparison to the time spent on computing (non-bonded) forces and neighbor lists.
Because r-RESPA decomposes the force computation, any interactions that involve lighter atoms, must be used at the inner level and only interactions between the heavy particles can be computed at the outer level. So, unless the number of heavy/slow particles is large compared to the number of light/fast particles, the savings are likely limited.
Please check it yourself. This is not an input file validation forum. As a scientist you should be capable of constructing different scenarios that would either produce the same or different output / forces depending on how r-RESPA is applied or not. Please note that with just one level, r-RESPA will degenerate to a velocity Verlet algorithm.