Does anyone know whether or not fruit trees can be sterile?

Not sterile, Dondebut, but it might be pining for a boy/girl friend. Some top fruit trees need a similar tree in the vicinity to cross polinate the flowers.

There is an old saying here in England that we grow pears for our heirs, your pear may have had the odd flowers on which the pollen has not set.

Pears take several years to settle down and start cropping - typically ten! Mine took nineteen!!

sounds interesting, maybe you lot can help out with my lemon tree question cheers