L'il gun is too fast a powder to be using in the .223, and Re 10 is too slow for enough to fit in a Fireball case. That's why we have so many powders. If you absolutely had to, you could safely load a Fireball charge in a .223 case. You'd be giving up several hundred fps from a normal .223 load. If you absolutely had to, you could safely load a Fireball case with Re 10 up to the base of the neck and seat a 50 grain bullet. Again, you would be giving up velocity.
The loading manuals list the useful loads for a cartridge. If a powder is not listed for a particular cartridge, there's a good reason for it, but not necessarily a safely issue.