Citrus Issue

This picture appears to be a sucker off of the rootstock. Special rootstocks are used to give a citrus tree a strong root system and are not intended to bear fruit. You can tell by where they come from. If they come from under the soil or below the graft union, they are rootstock. You will want to remove them to give your tree increased vigor. The suckers are also more susceptible to diseases and pests. This sucker might be exhibiting some citrus leafminer damage.
Another questions we would have is: did your citrus tree produce any flowers at all in the last year? If not, there might be a watering or a nutritional problem. Successful flowering is what leads to successful fruiting. You might want to visit your local independent garden center with a bagged sample of your tree to see what information they can give you. You should also be able to purchase a fertilizer formulated especially for Citrus. Use following directions on the label.