Britishgirl - hi.
How long ago was the blossoms on the Lemon and Lime? Did you get them from the nursery with the blossoms and then transplant them, or did the blossoms emerge after the transplant - or was the
tree already in the ground for a period of time?
These
trees are not the fastest for setting fruit and generally - fruit has to "winter" on the
tree. What that means is that this year's blossoms are next year's fruit. The reading I've done - says that all citrus is this way - and that grapefruit (I know you didn't say you had grapefruit

- but just had this discussion with someone at work wanting answers) is the fastest from blossom to fruit - and that is 9 months.
Also - - what is your average winter temperatures? Any freezing temps? The fruit has to be protected - to include the blossoms. Unlike "normal" fruit - - citrus really doesn't need "chill factor". There are things you can do for that too - - so let us know more about the
trees.
Jon