Well they can breed together. But the offspring will be infertile (not able to reproduce)The offspring
Offspring of a male lion and female tiger is called a liger
Offsrping of a Male tiger and a female lion is called a Tigon
Ligers tend to be larger than their parents and others in their species while Tigons are Smaller and no bigger than their parents.
Both Ligers and Tigons Tend to be Steril, but every now and again a female will be fertile (no record of males being fertile) and this is because of some lucky gene protein match up. And the female will be able to bred back to a male lion or tiger.
the fertile Female liger or Tigon can reproduce as follows into a new speices.
Lion + liger = li-liger
Lion + tigon = li-tigon
Tiger + liger = ti-liger
Tiger + tigon = ti-tigon