Is there a definition of species where Lions and Tigers are the same species?
The concept this would fit under would be the "Biological Species Concept."

Concerning this concept, the Evolution site for Berkeley says "members of populations that actually or potentially interbreed in nature..." constitute a species. By this definition, since lions and tigers can (and do) interbreed, they would be considered the same species under this concept.

EDIT: As Bryan pointed out, though, lions and tigers do not breed outside of captivity. NatGeo and Britannica both second this. With this, then, the Biological Species Concept would not be viable.

EDIT2: With the above in mind, there don’t seem to be many options.

Mate-Recognition: This idea posits that organisms who “recognize one another as potential mates” (Wikipedia, “Species”) make up a species. By this, it could be argued lions and tigers are the same species, but I would be hesitant for this to be the concept, for the same reasons against the Biological Species Concept (not occurring in nature).

Ecological: Using this definition, a species is made up “of organisms adapted to a particular... niche, in the environment” (Wikipedia). Again, this is very fuzzy, as I wouldn’t define them in the same niche (though this might depend on how specific you get).

Conclusion: These seem to be the most likely, though that’s a very loose term. I couldn’t find any others that would fit nearly as well. I would say the answer is “no”, but I don’t think I found all of the concepts.