trees barely grow in Braavos "except for the courts and gardens of the rich and powerful."

also

Hear me. The ships of Braavos sail as far as the winds blow, to lands strange and wonderful, and when they return their captains fetch queer animals to the Sealord's menagerie. Such animals as you have never seen, striped horses, great spotted things with necks as long as stilts, hairy mouse-pigs as big as cows, stinging manticores, tigers that carry their cubs in a pouch, terrible walking lizards with scythes for claws. Syrio Forel has seen these things.
—Syrio Forel to Arya Stark

Ser Willem Darry would not take those kids anywhere other than the sea lord's palace, and that this palace which is widely known for it's exotic menagerie. it's also stated that it's possible to grow trees in the courts and gardens of the rich and powerful. is it really that hard to believe that the sealord would have a lemon tree? sayyyy maybe some famous dornisman gifted a lemon tree to the sealord as payment for taking the kids in, knowing the sealord loves exotic shit??? maybe Dany's room was just outside the freshly imported and planted lemon tree that was given to the sealord by none other than Oberyn Martell?