First up, the Lucario starter must be given out as a Riolu. Secondly, a Fighting type can be used as a starter provided the other two types are Steel and Fairy as those three form the same relationship as Grass, Fire and Water. The big problem with using Riolu as your Fighting-type starter if you go down this road is it gains the Steel type when it evolves. A solution to that would be to adopt the Generation-VI secondary starter types as your starter trinity; consisting of Fighting, Psychic and Dark as they too have a similar triangular relationship.
Another issue is that starter Pokémon are generally able to evolve twice, have a gender ratio of 87.5% male/12.5% female and have a medium-slow growth rate. Riolu can only evolve once so outside of the Mystery Dungeon games, it is not a typical starter. Fighting types that can fit the starter mould would be Machop and Timburr (with an alteration regarding evolution to their final forms). For Steel, you can be quirky and have Aron (for patient trainers) or Klink (immune to Attract and Captivate, but evolves later); and for Fairy…I'd say Ralts, but one of its final evolutions is also a Fighting-type so that one's out. This leaves Flabébé with the caveat of changing the way Floette evolves from using a Shiny Stone to levelling up past a set threshold.