In my experience lime trees are excellent for honey bees.
However, they do need the right weather: the flower is an open bell hanging downwards, and hot dry weather will dry up the nectar. Bees will frequently be happy working them early in the morning, but then get bad tempered by 10am as the day becomes hot and dry. Wet or humid weather is less of a problem as there is nectar all day.
Stratford-upon-Avon has many lime trees and my apiary in the town often does very well from them.
A friend who lived (and kept bees) in Birmingham often migrated his father's bees from Wales to Birmingham when the limes were in flower just to give them a boost. (Birmingham has huge numbers of limes in the suburbs.)
Best wishes
Peter
52°14'44.44"N, 1°50'35"W
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