It depends on how many carbons you want to add and how you want to position them (random or not). You can define a unit cell including a carbon and then repeat it to make a super-cell. In that case C positions won't be random, though. You can also build a super-cell using a python script and then use read_data command in lammps script.

How can I make unit cell of Fe atoms including carbon atoms on its interstitial sites?

It can be done in many ways. You can use lattice custom command to define three basis atoms (two for Fe and one for C) in the lattice and then use create_atoms command using the basis argument (create_atoms 1 box & basis 3 2) to assign atom type 2 for the third basis atom. Thus, you can generate a custom unit cell with two types of atoms and then you can use replicate command to make the super cell.

Thank You Uttam Pal