A reasonable simple definition of a species would be where a male and female can produce offspring that is also capable of reproducing.
What if they they are biologically capable of producing fertile offspring -- for instance if "fooled" into mating by humans masking or faking certain signals between the sexes, or switching mates at the last minute, various methods are used -- but they never do so on their own, in the natural state? What if they can't physically mate, but can be crossed by artificial means? What if the hybrids are biologically fertile, but not actually successful in mating in nature (because they lack proper markings, behaviors, or for any number of reasons)? What if they are merely relatively less successful in mating or rearing such that their lineages invariably "peter out" and have no actual biological effect on populations of either species? What if they invariably back-cross and "revert to type," again having no real population effects. What if the hybrids can mate successfully, but not bring offspring fully to term, or successfully rear them, etc? Or what if their fertility is merely reduced to one of any number of degrees? What if hybrids are not inter-fertile with each other, but are with either of the parent species? What if they're inter-fertile with one of the parent species, but not the other?
All of these "what ifs" (and many more) are instantiated in nature.
In short, your definition is not "simple". None is. Even though there clearly are such things as "species," there is no single "simple," sufficient and universal criteria for distinguishing them. There shouldn't be because they are ultimately connected by continua (even if most elements thereof end up being eliminated) and separated from one another in infinitely varying degrees.
So lions and tigers are the same species, then.