We had a Lahsa, same thing wouldn't chase anything, but would bark endlessly at rocks!
But my doxie is a better mouser then a cat (sadly he has a taste for chicken too so we erected the "Tucker can't eat any more of my chickens fence") And we have a new rescue not sure what she is mixed w/ but probably some jack russel and hound (bird dog ish) full of energy will chase anything, but unlike my doxie won't hurt it, just loves the chase.