I have a dwarf grafted citrus in a pot in my garden. The trunk is grafted with one lemon branch and one lime branch. Over the last two years the lemon half of the tree has grown well and fruited several times, while the lime half has not grown at all, and the few tiny fruit that develop after flowering drop off after about a week.
The tree is potted in a well known brand of citrus potting compost, and I've added a small amount of slow release citrus fertiliser periodically.
Here are some photos of the graft and the tree itself - the lime is the thin branch on the right in both:
What can I do to encourage the lime side of the tree to grow and produce fruit?